ARITHMETICS 


FUNDAMENTAL  PROCESSES 


STATE  NORMAL  SCHOOL 

LQ8 


• 


WALSH-SUZZALLO 
ARITHMETICS 

BOOK  ONE 

FUNDAMENTAL  PROCESSES 


BT 
JOHN   H.   WALSH 

ASSOCIATE    SUPERINTENDENT   OF   SCHOOLS 
THE    CITY    OF    NEW  YORK 


PROFESSOR    OF    THE    PHILOSOPHY    OF   EDUCATION 
TEACHERS    COLLEGE,    COLUMBIA    UNIVERSITY 


D.    C.    HEATH   &   CO.,  PUBLISHERS 
BOSTON  NEW  YORK  CHICAGO 

3 


COPYRIGHT,  1914, 
BY  D.  C.  HEATH  &  Co. 

IBS 


PREFACE 

THESE  books  are  designed  to  give  an  elementary  school 
child  all  the  arithmetical  power  necessary  to  cope  with 
the  situations  of  common  everyday  life.  A  social  survey 
of  the  usual  responsibilities  of  men  has  determined  omis- 
sions and  additions.  The  methods  of  learning  and  teach- 
ing employed  have  been  indicated  by  an  analysis  of 
thousands  of  typical  arithmetical  errors  collected  in  ordi- 
nary schools. 

Because  a  standard  of  social  efficiency  has  been  applied 
throughout,  it  is  expected  that  the  immediate  competency 
of  the  pupil  leaving  school  will  be  greatly  increased. 
Because  a  standard  of  pedagogical  economy  has  likewise 
been  rigidly  observed,  it  is  also  expected  that  the  pupils 
will  develop  this  competency  one  to  two  years  earlier. 

In  consequence,  this  series  has  been  so  arranged  that  a 
child  may  acquire  an  easy  and  accurate  command  over  all 
fundamental  processes,  both  simple  and  complex,  by  the 
end  of  the  sixth  year.  The  seventh  and  eighth  school 
years  are  thus  left  free  for  a  study  of  those  business  insti- 
tutions and  practices,  the  understanding  of  which  is  vital 
to  an  extended  use  of  arithmetic  in  practical  life. 

This  particular  book,  the  first  one  in  the  series,  covers 


iv  PREFACE 

the  fundamental  elements  of  arithmetical  manipulation 
and  thought.  Thus  a  child  who  goes  no  farther  than  the 
fourth  or  fifth  grade  will  be  so  familiar  with  essentials 
that  he  can  readily  learn  more  arithmetic  by  himself. 

No  attempt  has  been  made  to  project  the  pupil  into 
unfamiliar  situations.  His  experience  is  already  greater 
than  his  power  of  mathematical  interpretation.  The 
teacher  of  primary  arithmetic  has  accomplished  enough 
when  she  has  taught  the  child  to  solve  his  own  problems. 
Hence,  a  special  effort  has  been  made  to  keep  both  exam- 
ples and  problems  within  the  reach  of  the  child. 

While  abstract  work  is  the  chief  difficulty  of  the  first 
school  grades,  it  must  ever  be  remembered  that  it  is 
always  a  concrete  and  personally  vital  problem  which  pro- 
vokes the  need  to  compute.  In  all  development  of  new 
technique,  the  teacher  should  start  with  an  easy  problem 
actually  or  orally  expressed.  Once  the  child  has  decided 
from  the  concrete  situation  what  he  is  to  do,  he  should  be 
permitted  to  do  it  symbolically  or  abstractly.  Mere 
drill  on  combinations,  processes,  and  manipulations  may 
well  be  abstract,  provided  the  pupil  feels  the  need  of  such 
perfection  and  knows  that  in  the  end  his  facility  is  to  be 
used  in  the  solution  of  real  problems. 

In  this  text,  every  new  process  is  introduced  by  a  prob- 
lem that  calls  for  its  use.  Similarly,  the  last  drill  upon  a 
process  is  given  in  the  form  of  oral  and  written  problems. 
This  is  to  remind  the  teacher  that  all  abstract  work,  how- 
ever important,  is  merely  an  intermediate  stage  in  the 


PREFACE  v 

effective  teaching  of  arithmetic.  Ample  provision  must 
be  made  for  concrete  work  at  the  beginning  and  end  of  all 
practice  upon  the  mechanics  of  arithmetic. 

The  use  of  more  than  one  way  of  working  an  example 
has  been  carefully  avoided.  We  should  be  content  with 
one  concrete  method  of  computation,  particularly  in  the 
primary  grades.  To  attempt  to  develop  two  different 
habits  of  response  to  the  same  situation  leads  to  confusion 
and  waste.  Short  methods  of  operation  are  given  only 
in  the  higher  grades. 

Special  attention  is  called  to  the  device  used  to  give  the 
child  a  clear  understanding  of  the  manner  in  which  formal 
processes  are  performed.  Whenever  a  process  is  expressed 
in  figures,  each  stage  of  the  mental  process  accompanying 
it  is  also  expressed  in  simple  language.  These  parallel 
language  statements  take  the  form  of  simple  directions 
given  in  the  most  economical  and  efficient  order.  If  the 
child  does  not  clearly  see  how  the  process  has  been  con- 
ducted in  the  course  of  the  teacher's  demonstration,  refer- 
ence to  the  text  makes  it  clear.  In  establishing  a  habit 
it  is  advantageous  to  follow  an  accurate,  permanent,  and 
consistent  form.  It  is  quite  impossible  for  the  teacher 
to  give  a  great  amount  of  attention  to  each  individual  in 
our  large  classes,  and  it  is  wise  to  develop  in  the  child 
the  power  to  understand  and  practice  arithmetical  manipu- 
lations by  himself.  In  line  with  this  effort  to  give  the 
child  power  to  care  for  himself,  the  child  is  constantly 
taught  to  test  or  check  his  work. 


iv  PREFACE 

the  fundamental  elements  of  arithmetical  manipulation 
and  thought.  Thus  a  child  who  goes  no  farther  than  the 
fourth  or  fifth  grade  will  be  so  familiar  with  essentials 
that  he  can  readily  learn  more  arithmetic  by  himself. 

No  attempt  has  been  made  to  project  the  pupil  into 
unfamiliar  situations.  His  experience  is  already  greater 
than  his  power  of  mathematical  interpretation.  The 
teacher  of  primary  arithmetic  has  accomplished  enough 
when  she  has  taught  the  child  to  solve  his  own  problems. 
Hence,  a  special  effort  has  been  made  to  keep  both  exam- 
ples and  problems  within  the  reach  of  the  child. 

While  abstract  work  is  the  chief  difficulty  of  the  first 
school  grades,  it  must  ever  be  remembered  that  it  is 
always  a  concrete  and  personally  vital  problem  which  pro- 
vokes the  need  to  compute.  In  all  development  of  new 
technique,  the  teacher  should  start  with  an  easy  problem 
actually  or  orally  expressed.  Once  the  child  has  decided 
from  the  concrete  situation  what  he  is  to  do,  he  should  be 
permitted  to  do  it  symbolically  or  abstractly.  Mere 
drill  on  combinations,  processes,  and  manipulations  may 
well  be  abstract,  provided  the  pupil  feels  the  need  of  such 
perfection  and  knows  that  in  the  end  his  facility  is  to  be 
used  in  the  solution  of  real  problems. 

In  this  text,  every  new  process  is  introduced  by  a  prob- 
lem that  calls  for  its  use.  Similarly,  the  last  drill  upon  a 
process  is  given  in  the  form  of  oral  and  written  problems. 
This  is  to  remind  the  teacher  that  all  abstract  work,  how- 
ever important,  is  merely  an  intermediate  stage  in  the 


PREFACE  v 

effective  teaching  of  arithmetic.  Ample  provision  must 
be  made  for  concrete  work  at  the  beginning  and  end  of  all 
practice  upon  the  mechanics  of  arithmetic. 

The  use  of  more  than  one  way  of  working  an  example 
has  been  carefully  avoided.  We  should  be  content  with 
one  concrete  method  of  computation,  particularly  in  the 
primary  grades.  To  attempt  to  develop  two  different 
habits  of  response  to  the  same  situation  leads  to  confusion 
and  waste.  Short  methods  of  operation  are  given  only 
in  the  higher  grades. 

Special  attention  is  called  to  the  device  used  to  give  the 
child  a  clear  understanding  of  the  manner  in  which  formal 
processes  are  performed.  Whenever  a  process  is  expressed 
in  figures,  each  stage  of  the  mental  process  accompanying 
it  is  also  expressed  in  simple  language.  These  parallel 
language  statements  take  the  form  of  simple  directions 
given  in  the  most  economical  and  efficient  order.  If  the 
child  does  not  clearly  see  how  the  process  has  been  con- 
ducted in  the  course  of  the  teacher's  demonstration,  refer- 
ence to  the  text  makes  it  clear.  In  establishing  a  habit 
it  is  advantageous  to  follow  an  accurate,  permanent,  and 
consistent  form.  It  is  quite  impossible  for  the  teacher 
to  give  a  great  amount  of  attention  to  each  individual  in 
our  large  classes,  and  it  is  wise  to  develop  in  the  child 
the  power  to  understand  and  practice  arithmetical  manipu- 
lations by  himself.  In  line  with  this  effort  to  give  the 
child  power  to  care  for  himself,  the  child  is  constantly 
taught  to  test  or  check  his  work. 


vi  PREFACE 

These  texts  are  not  a  substitute  for  a  good  teacher; 
they  are  an  important  and  necessary  aid.  They  aim  to  be 
efficient  and  economical  guides  to  both  teacher  and  pupil. 
The  topics,  problems,  and  processes  are  representative  of 
the  arithmetical  facts,  power,  and  skill  that  will  be 
most  useful  to  the  average  citizen.  The  methods  of  treat- 
ing them  have  been  garnered  from  the  most  successful 
teaching  practice. 


CONTENTS 


SECTION   ONE  —  PRELIMINARY  REVIEW 


I'AOK 
1 

2 
2 
3 
4 


COUNTING 

ADDING  BY  ONES  .  . 
READING  NUMBERS  .  . 
ADDING  BY  Twos  .  . 

TREASURING 

READING     AND     WRITING 

NUMBERS 6 

ADDING  BY  THREES  ...  6 
ADDING  BY  FOURS  ...  7 
ADDING  BY  FIVES  ...  8 

MEASURING 9 

WRITTEN  ADDITION  ...  11 
MAKING  CHANGE  ....  13 
SUBTRACTION  14 


NOTATION   AND    NUMERA- 
TION   20 

ADDING  BY  6's.    BY  7's    .  21 
ADDING  BY  8's.    BY  9's    .  22 
ADDITION,    WITH    CARRY- 
ING      24 

TESTING  RESULTS     ...  25 

ONE  HALF.  ONE  QUARTER  26 

ROMAN  NUMBERS      ...  27 

TELLING  TIME 27 

EQUAL  PARTS 30 

QUART  AND  PECK     ...  30 
SUBTRACTION,  WITH   CAR- 
RYING      31 


MULTIPLYING  BY  2 
DIVIDING  BY  2 
MULTIPLYING  BY  3 
DIVIDING  BY  3 
MULTIPLYING  BY  4 
DIVIDING  BY  4 
MULTIPLYING  BY  5 


SECTION   TWO 

.    .      35  DIVIDING  BY  5      ....  53 

.    .      40  LIQUID  MEASURE.    ...  54 

.    .      44      RECTANGLES 55 

.    .      45      TIME 58 

.    .      48  ROMAN  NUMBERS      ...  58 

.    .      49  NOTATION   AND    NUMEUA- 

52         TION 59 


Vlll 


CONTENTS 


PAOB 

ROMAN  NUMBERS      ...  61 

DOLLARS  AND  CENTS    .    .  62 

ADDITION  OF  MONEY     .    .  64 

SUBTRACTION  OF  MONEY  .  66 

FUNDAMENTAL  OPERATIONS  67 

MULTIPLICATION  TABLE    .  70 

MULTIPLYING  BY  6   ...  72 

DIVIDING  BY  6      ....  73 

REMAINDERS   IN   DIVISION  75 

MULTIPLYING  BY  7    ...  78 

DIVIDING  BY  7      ....  79 

MULTIPLYING  BY  8.     BY  9  82 

DIVIDING  BY  8.     BY  9  .  83 


PROBLEMS      WITH       Two 

OPERATIONS 84 

MULTIPLYING  BY  10      .    .  88 
DIVIDING  BY  10    ....  88 
MULTIPLYING  BY  A   MUL- 
TIPLE OF  10 89 

DIVIDING  BY  A  MULTIPLE 

OF  10 91 

INEXACT  DIVISION    ...  92 

AREAS  OF  RECTANGLES     .  93 

FRACTIONAL  PARTS  ...  94 

DENOMINATE  NUMBERS      .  96 

RECTANGULAR  SOLIDS  .    .  98 


SECTION  THREE 


READING     AND     WRITING 

NUMBERS  ....'..  99 

MULTIPLIERS  OF  Two  FIG- 
URES        100 

LONG  DIVISION     ....  104 

PROBLEMS      WITH      MORE 

THAN  ONE  OPERATION  .  106 

LONG  DIVISION     ....  108 

ADDITION   AND    SUBTRAC- 
TION    109 

ADDING  AND  SUBTRACTING 

DOLLARS  AND  CENTS     .  112 

CENTS  AS  DIVISORS  .    .    .  114 

URING  RECTANGLES  .  115 

FRACTIONAL  PARTS  .  120 


MIXED  NUMBERS  CONTAIN- 
ING HALVES 122 

ADDING  AND  SUBTRACTING 

MIXED  NUMBERS  .     .     .  123 

HALVES  AND  FOURTHS  .     .  125 

THIRDS  AND  SIXTHS      .     .  129 

RATIO 132 

FIFTHS 133 

MULTIPLYING  AND  DIVID- 
ING BY  11 145 

MULTIPLYING  'AND  DIVID- 
ING BY  12 146 

MULTIPLIERS    CONTAINING 

CIPHERS 148 

LONG  DIVISION     ....  151 


CONTENTS 


IX 


PAGE 

MULTIPLES  AND   FACTORS  158 
REDUCTION       OF       FRAC- 
TIONS   159 

ADDING  AND  SUBTRACTING 

FRACTIONS 160 

ADDING  MIXED  NUMBERS  161 
SUBTRACTING  MIXED  NUM- 
BERS        162 


FRACTIONAL  PARTS  OF 
NUMBERS 165 

MULTIPLYING  BY  A  MIXED 
NUMBER 167 

LONG  MEASURE    ....    174"^ 

AREAS 

SQUARE  MEASURE     .    .    . 

CUBICAL  CONTENTS  .  179 


SECTION  FOUR 


NOTATION   AND    NUMERA- 
TION   183 

ADDITION    AND    SUBTRAC- 
TION    185 

MULTIPLICATION  AND   DI- 
VISION     188 

WRITTEN  MULTIPLICATION  190 

LONG  DIVISION     ....  191 
ALIQUOT  PARTS  OP  A  DOLLAR  196 

CANCELLATION 198 

FRACTIONS 201 

PROPER     AND     IMPROPER 

FRACTIONS 205 

LOWEST   TERMS.    HIGHER 

TERMS 206 

COMMON  DENOMINATORS   .  207 
ADDITION  OF  FRACTIONS  .  208 
ADDITION  OF  MIXED  NUM- 
BERS    209 


SUBTRACTION    OF    MIXED 

NUMBERS 210 

PRODUCT     OF     A     MIXED 
NUMBER  AND  A  WHOLE 

NUMBER 214 

MULTIPLICATION  OF  FRAC- 
TIONS      218 

DIVISION  OF  FRACTIONS    .     220 
FRACTIONAL  RELATIONS    .    222 

DECIMALS 225 

DECIMAL    NOTATION    AND 

NUMERATION     ....    226 
READING     AND     WRITING 

DECIMALS 227 

REDUCTION  OF  DECIMALS.    227 
MULTIPLYING  A   DECIMAL 

BY  A  WHOLE  NUMBER  .    229 
DIVIDING  A   DECIMAL   BY 
A  WHOLE  NUMBER  229 


x  CONTENTS 

PAGE  PACE 

ADDITION   AMD   SUBTRAO  BILLS 236 

TION  OF  DECIMALS    .    .    230  LETTERS 240 

COMPOUND  NUMBERS    .    .    233  CHECKS 241 

MEASUREMENTS     ....    234  NOTES 242 

VOLUMES 235  RECEIPTS 242 

BUSINESS  FORMS  .  ,    236  ACCOUNTS  244 


ARITHMETIC 


FIRST   BOOK 
SECTION  I 

INTRODUCTORY  REVIEW 
Counting 

1.  How  many  men  are  there  in  the  picture  on  the 
left-hand  page  ? 

2.  How  many  children  ? 

3.  How  many  horses  ? 

4.  How  many  cows  ? 

5.  How  many  sheep  ? 

6.  How  many  hens  ?      \ 

7.  How  many  ducks  ?  >, 

8.  How  many  pigeons  are  there  in  the  picture  ? 

9.  How  many  doors  has  our  class  room  ? 

10.  How  many  windows  ? 

11.  How  many  panes  of  glass  are  there  in  each 
window  ? 

12    How  many  rows  of  desks  are  there  ? 
13.    How  many  desks  are  there  in  each  row  ? 


SECTION   ONE 


Adding  by  Ones 

1.  Sarah  has  two  girl  dolls  and  one 
boy  doll.     How  many  dolls  has  she  ? 

2.  William  has  three  pears  in  his 
basket  and  one   pear   in   his   hand. 
How  many  pears  has  he  ? 

3.  Of  a  flock  of  geese,  four  are  in 
the  pond  and  one  is  on  the  bank.    How 
many  geese  are  there  in   the  flock  ? 

4.  Jane  spent  five  cents  for  a  pencil 
and  one  cent  for  a  pen.      How  many  cents  did  she 
spend  for  both  ? 

5.    John  has  six  cents.      If  his  father  gives  him 
one  cent,  how  many  cents  will  he  have  ? 

Reading  Numbers 


One      Two      Three      Four      Five      Six      Seven      Eight    Nine     Ten 

123        4567        89      10 


a. 


Sight  Drills 
Give  sums  rapidly : 

111111111 
123456789 


INTRODUCTORY   REVIEW 

Adding  by  Twos 

1.  Arthur  has  two  large  rockets 
and  two  small  ones.      How  many 
rockets  has  he  ? 

2.  How  many  are  two  and  two  ? 

3.  Ann  rode  three  miles  on  the 
cars  and   two  miles   in   the    stage. 
How  many  miles  did  she  ride  ? 

4.  How  many  are  three  and  two  ? 
2  and  3? 

5.  Fred   has   four   cents    in   his 

bank.     How  many  cents  will  be  in  the  bank  after 
he  puts  into  it  two  more  cents? 

6.  How  many  are  four  and  two  ?     2  and  4  ? 

7.  There  are  five  pears  on  one  plate  and  two  on 
another.     How  many  pears  are  there  on  both  plates  ? 

s.    How  many  are  five  and  two  ?     2  and  5  ? 

9.    Helen  found  six  eggs  in  one  nest  and  two  in 
another.     How  many  eggs  did  she  find  ? 

10.  How  many  are  six  and  two  ?     2  and  6  ? 

11.  Harry  is  seven  years  old  and  his  sister  Mary  is 
two  years  older.     How  old  is  Mary  ? 

12.  How  many  are  seven  and  two  ?     2  and  7  ? 

13.  There   are   eight   children   now   in  the  room. 
How  many  will  there  be  when  two  more  come  ? 

14.  How  many  are  eight  and  two  ?     2  and  8  ? 


4  SECTION  ONE 

Measuring 

1.  How  many  steps  across  the  class  room  ? 

2.  How  many  steps  are  there  in  the  length  of 
the  class  room  ? 

3.  How  many  glassfuls  will  the  pitcher  hold  ? 

4.  How  many  pitcherf  uls  will  the  pail  hold  ? 

5.  How  many  glassfuls  will  the  pint  hold  ? 

6.  How  many  pints  will  the  quart  hold  ? 

7.  How  many  quarts  will  the  pitcher  hold  ? 

8.  How  many  quarts  will  the  pail  hold  ? 

Playing  Store 

9.  Use  cents  to  pay  for  articles  costing : 

(a)  Four  cents ;    (6)  six  cents ;     (c)  three  cents ; 
(d)  Two  cents ;    (e)  five  cents ;  (/)  seven  cents. 

10.  How  many  cents  are  there  in  a  nickel  ? 

11.  Using  a  nickel  and  cents,  pay  for  articles  cost- 
ing :     (a)  Six  cents ;     (6)  eight  cents ;    (c)  ten  cents ; 
(d)  nine  cents ;  (e)  seven  cents. 

12.  How  many  cents  are  there  in  a  dime  ? 
is.    How  many  nickels  are  there  in  a  dime  ? 
14.    How  many  cents  are  there  in  two  nickels  ? 

is.    If  you  have  three  cents  and  a  nickel  in  your 
pocket  how  many  cents  have  you  ? 

16.  If  you  have  one  cent  and  a  nickel  ? 

17.  If  you  have  four  cents  and  a  nickel  ? 
is.    If  you  have  two  cents  and  a  nickel  ? 


INTRODUCTORY  REVIEW  5 

Reading  and  Writing  Numbers 

Ten  is  written  10.  Eleven  is  written  11. 

Twelve  is  written  12.  Thirteen  is  written  13. 

Write  :  Fourteen ;  fifteen  ;  sixteen  ;  seventeen ; 
eighteen ;  nineteen. 

Read  the  following : 
16,        18,        13,        19,        15,        12,        10,        14. 

i.  How  many  cents  in  a  dime  ?  In  two  dimes  ? 
In  three  dimes  ?  In  four  dimes  ?  In  five  dimes  ? 
In  six  dimes?  In  seven  dimes?  In  eight  dimes? 
In  nine  dimes  ? 

Twenty  is  written  20.  Thirty  is  written  30. 

Forty  is  written  40.  Fifty  is  written  50. 

Write :  Sixty ;  seventy ;  eighty ;  ninety. 
Twenty-one  is  written  21.  Fifty-four  is  written  54. 
Forty-three  is  written  43.  Thirty-two  is  written  32. 

Read  the  following: 
22,       33,        44,       51,       65,        78,        86,        92. 


The  right-hand  figure  of  a  number  is  called  the 
ones'  figure. 


Drill  Exercises 


Add: 

a. 

2 

6 

2 

3 

2 

4 

2 

10 

8 

2 

9 

2 

5 

2 

7 

2 

1). 

7 

2 

5 

2 

8 

2 

9 

2 

2 

6 

2 

4 

2 

3 

2 

10 

6 


SECTION  ONE 


Adding  by  Threes 

1.  There  are  three  roses  on 
one  bush  and  three  on  another 
bush.      How    many    roses    are 
there  on  both  bushes  ? 

2.  How  many  are  three  and 
three  ? 

3.  Mr.  Smith  sold  four  pigs  to  one  man  and  three 
to  another.     How  many  pigs  did  he  sell  ? 

4.  How  many  are  four  and  three  ?    3  and  4  ? 

5.  A  girl  spent  five  cents  for  ice  cream  and  three 
cents  for  cake.     How  much  did  she  spend  ? 

6.  How  many  are  five  and  three  ?     3  and  5  ? 

7.  There  are  six  quarts  of  milk  in  one  can  and 
three  quarts  in  another.    How  many  quarts  are  there 
in  both  cans  ? 

8.  How  many  are  six  and  three  ?     3  and  6  ? 

9.  Frank  has  seven  hens  and  three  ducks.     How 
many  has  he  of  both  ? 

10.  How  many  are  seven  and  three?     3  and  7  ? 

11.  How  many  fish  are  in  a  jar  if  there  are  eight 
gold  fish  and  three  silver  fish  in  it  ? 

12.  How  many  are  eight  and  three  ?     3  and  8  ? 

is.    Ned  has  nine  marbles  in  a  bag  and  three  in  his 
pocket.     How  many  marbles  has  he  ? 

14.   How  many  are  nine  and  three?     3  and  9  ? 


INTRODUCTORY  REVIEW  7 

Adding  by  Fours 

1.  There  are  four  boys  and  four  girls  in  a  car. 
How  many  children  are  there  in  the  car  ? 

2.  How  many  are  four  and  four  ? 

3.  A  girl  has  a  five-cent  piece  and  four  pennies  in 
her  bank.     How  much  money  is  there  in  the  bank  ? 

4.  How  many  are  five  and  four  ?     4  and  5  ? 

5.  Along  the  walk  there  are  six  maple  trees  and 
four  elms.     How  many  trees  are  there  ? 

6.  How  many  are  six  and  four  ?      4  and  6  ? 

7.  James  has  seven  pounds  of  flour  in  his  basket. 
The  basket  weighs  four  pounds.     How  many  pounds 
do  both  weigh  ? 

s.    How  many  are  seven  and  four  ?      4  and  7  ? 

9.   Mary  is  eight  years  old.     Her  brother  is  four 
years  older.     How  old  is  her  brother  ? 

10.  How  many  are  eight  and  four  ?      4  and  8  ? 

11.  If  a  book  cost  nine  cents  and  a  pad  cost  four 
cents,  how  much  will  both  cost  ? 

12.  How  many  are  nine  and  4  ?     4  and  9  ? 

Counting 

1.  Count  by  2's  to  twenty.     By  3's  to  eighteen. 
By  4's  to  twenty.    By  5's  to  ninety.    By  10's  to  ninety. 

2.  Count  by  2's  to  eight,  then  by  4's  to  twenty. 

3.  Count  by  3's  to  fifteen,  then  by  5's  to  forty. 


8  SECTION   ONE 

Adding  by  Fives 

1.  A  boy  has  five  marbles  in  one  hand  and  five 
in  the  other.     How  many  has  he  in  both  hands  ? 

2.  How  many  are  five  and  five  ? 

3.  One  hen  has  six  chickens,  and  another  hen 
has  five.     How  many  chickens  have  both  hens  ? 

4.  How  many  are  six  and  five  ?     5  and  6  ? 

5.  It  is  now  seven  o'clock.     What  time  will  it  be 
in  five  hours? 

6.  How  many  are  seven  and  five  ?     5  and  7  ? 

7.  John  picks  eight  quarts  of  berries  and  Thomas 
picks  five  quarts.     How  many  quarts  do  both  boys 
pick? 

8.  How  many  are  eight  and  five?     5  and  8  ? 

9.  My  peach  tree  is  nine  feet  high  and  my  pear 
tree  is  five  feet  higher.     How  high  is  the  pear  tree  ? 

10.  How  many  are  nine  and  five?    5  and  9  ? 

11.  John  took  five  steps  to  the  right  and  then  four 
steps  straight  ahead.     How  many  steps  did  he  take  ? 

12.  How  many  are  four  and  five  ?     5  and  four  ? 


INTRODUCTORY  REVIEW  9 


Sight  Drills 
Give  answers  rapidly : 


A 

£ 

c 

D 

E 

F 

G 

H 

/ 

a. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

4 

4 

4 

4 

4 

4 

4 

4 

4 

b. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

5 

5 

5 

5 

5 

5 

5 

5 

5 

c. 

4 

4 

4 

4 

4 

4 

4 

4 

4 

2 

5 

3 

6 

1 

7 

9 

0 

8 

d. 

5 

5 

5 

5 

5 

5 

5 

5 

5 

7 

1 

6 

8 

2 

4 

9 

0 

3 

Measuring 

1.  Measure  the  length  of  a  book  in  inches.     The 
width. 

2.  Measure  the  length  and  the  width  of  a  pane  of 
glass. 

3.  Find  the  length  of  the  class  room  in  feet.     Its 
breadth  in  feet. 

4.  Find  the  length  and  the  breadth  of  the  school 
yard  in  feet. 

5.  Find  the  dimensions  of    the   blackboard.     Of 
the  door.     Of  a  window. 

6.  How  many  inches  are  there  in  a  foot  ? 

7.  Find  the  number  of  inches  in  one  half  foot. 


10  SECTION  ONE 

Sight  Drills 
Give  sums.     Add  upward. 

E  F  G 

444 

54         64         74, 

666 

62          72         82 

88  8 

51         61         71 

777 
72         82         92 

432 
61         71         81 

676 
72         82         92 

215 
93         63         33 


443 

154 

54        60          71 

63  72  83 
245 
421 


A 

B 

c 

z> 

a.  4 

4 

4 

4 

14 

24 

34 

44 

b.  6 

6 

6 

6 

22 

32 

42 

52 

c.   8 

8 

8 

8 

11 

21 

31 

41 

d.  7 

7 

7 

7 

32 

42 

52 

62 

e.  8 

7 

6 

5 

21 

31 

41 

51 

/   2 

3 

4 

5 

32 

42 

52 

62 

9-  4 

5 

6 

3 

23 

.53 

43 

73 

Say  15, 

16;  25, 

29;  etc. 

h.   1 

4 

3 

1 

2 

1 

2 

2 

13 

24 

33 

44 

i.  21 

36 

44 

57 

7 

2 

1 

1 

1 

1 

2 

1 

INTRODUCTORY   REVIEW  11 

Addition 

Written  Exercises 
Add: 

Before  working  these  written  exercises,  give  orally 
,*he  sum  of  each  column  in  an  example,  beginning 
with  the  ones'  column. 


a. 


b. 


c. 


d. 


c. 


A 

B 

c 

D 

E 

F 

0 

24 

62 

71 

43 

25 

47 

23 

62 

36 

26 

34 

52 

22 

64 

61 

43 

18 

35 

63 

54 

47 

27 

36 

61 

54 

22 

33 

32 

74 

43 

28 

64 

53 

35 

65 

15 

45 

71 

35 

45 

24 

33 

11 

95 

63 

50 

32 

32 

23 

15 

2 

31 

14 

32 

23 

24 

32 

1 

5 

35 

32 

32 

32 

32 

21 

41 

21 

51 

22 

32 

22 

32 

5 

34 

3 

32 

32 

•  4 

23 

13 

4 

12 

42 

23 

""*" 

" 

~ 

~ 

12 

31 

41 

42 

23 

53 

32 

52 

41 

33 

16 

4 

3 

33 

4 

27 

5 

11 

31 

41 

32 

23 

12 

14 

4 

12 

62 

42 

23 

12 

3 

12 

3 

4 

3 

23 

12 

21 

61 

62 

3 

24 

12  SECTION  ONE 

Written  Problems 

i.    A  boy  earned  thirty  cents,  twenty-five  cents,  and 
three  cents.     How  much  did  he  earn  ? 


PROCESS  30c. 

Write  the  numbers  under  each  other,  placing  25 

the  ones'  figures  of  each  in  a  row.     Write  under  3 

each  column  its  sum.  Ans  58c 


2.    Add  forty  cents,  thirteen  cents,  and  six  cents. 

To  save  unnecessary  repetition,  write  c.  but  once 

in  the  example  and  again  in  the  answer. 

f» 

c.  stands  for  cents. 

Ans.  59  c. 


The  sign  of  addition  is  + ,  called  plus. 


3.   31  +  42  +  3  +  1.  4.    22  +  33  +  14. 

5.  Twenty-five  boys,  plus  twelve  boys,  plus  two 
boys. 

6.  Ten  cows,  plus  twenty-six  cows,  plus  three  cows. 

7.  A  farmer  has  twenty-four  cows  in  one  field  and 
fourteen  in  another  field.     How  many  cows  has  he  in 
both  fields  ? 

8.  Mr.  Smith  sold  eighteen  pies  Monday  and  eleven 
Tuesday.     How  many  did  he  sell  in  the  two  days  ? 

9.  A  boy  paid  twenty-five  cents  for  a   ball  and 
twelve  cents  for  a  bat.     How  much  did  he  pay  for 
both? 


INTRODUCTORY  REVIEW  13 

Making  Change 

Let  one  pupil  represent  a  storekeeper  and  another  a  cus- 
tomer. The  latter  announces  the  total  of  his  purchase,  giving 
money  to  the  former,  who  then  hands  over  the  change.  The 
customer  satisfies  himself  of  the  correctness  of  the  latter,  stat- 
ing its  amount.  He  then  becomes  the  storekeeper  and  a  third 
pupil  becomes  a  customer. 

Make  change  in  the  business  way.  If  a  half-dollar  is  given 
for  a  thirty -eight  cent  purchase,  the  storekeeper  hands  two  cents, 
saying  "thirty-eight,  forty" ;  then  a  dime,  saying  "fifty." 

Make  change  for  the  following  purchases  : 

1.  Amount  of  purchase,  6  cents.     Sum  given,  25 
cents. 

2.  Amount  of  purchase,  43  cents.     Sum  given,  50 
cents. 

3.  Amount  of  purchase,  11  cents.     Sum  given,  25 
cents. 

4.  Amount  of  purchase,  29  cents.     Sum  given,  35 
cents. 

5.  Amount  of  purchase,  68  cents.     Sum  given,  75 
cents. 

6.  Amount  of  purchase,  8  cents.     Sum  given,  50 
cents. 

7.  Amount  of  purchase,  17  cents.     Sum  given,  25 
cents. 

s.  Amount  of  purchase,  3  cents.  Sum  given,  25 
cents. 

9.  Amount  of  purchase,  27  cents.  Sum  given,  30 
cents. 


14  SECTION  ONE 

Subtraction.  —  Preparatory  Exercises 

1.  If  John  needs  10  cents  for  a  ball  and  he  al- 
ready has  5  cents,  how  many  more  cents  does  he  re- 
quire ? 

2.  What  number  added  to  7  will  make  14  ? 

3.  A  boy  placed  9  marbles  in  two   piles,  one  of 
which  contained  5  marbles.     How  many  were  there 
in  the  other  pile  ? 

4.  In  how  many  years  will  a  5-year  old  girl  be  8 
years  old? 

'•Is.  A  man  is  making  a  trip  of  6  miles.  If  he  has 
gone  2  miles  already,  how  many  miles  has  he  still  to 
go? 

6.  Mabel  and  Samuel  together  picked  8  quarts  of 
berries.     If  Samuel  picked  3  quarts,  how  many  quarts 
did  Mabel  pick? 

7.  Nine   boys  are  required  for  a  baseball   team. 
Only  six  have  been  chosen.     How  many  more  must 
they  have  ? 

a.  If  I  buy  7  cents'  worth  of  candy  and  give  the 
storekeeper  a  dime,  how  much  change  should  I 
receive  ? 

9.  There  were  10  trees  in  a  grove.  After  3  were 
cut  down,  how  many  were  left  standing  ? 

i  10.  William  rode  12  miles  in  an  automobile.  How 
many  more  miles  did  he  ride  than  Edwin,  who  rode 
only  8  miles  ? 


INTRODUCTORY  REVIEW  15 

Drill  Exercises 

Tell  the  number  that  must  be  added  to  the  lower 
one  to  make  the  upper  one : 

ABODE    F    G  H    I 

a.   9   8   2   9   3   7   4  9   8 

_1  _7  _i  _8  -1  -6  -2  -6  -1 


The  sign  of  subtraction  is  — ,  called  minus. 


Subtraction 
1.   From  86  take  32. 


I.   793856954 
_1  _7  _2  -6  -4  -3  -2  -1  -3 


c.   976847689 
-3  -5  -1  -5  -1  -2  -5  -2  -5 


d.   578675689 
-2  -3  -4  -2  -4  -3  -4  -3  -4 


PROCESS 

Write  32  under  86,  placing. the  ones' 
figures  of  both  in  the  same  column.     Begin  32 

at  the  ones'  column  and  think  2  and  4 
(writing  4)  are  6,  3  and  5  (writing  5)  are  8. 


16 


SECTION  ONE 
Written  Exercises 


The    answer    in   subtraction 
mainder. 

is   called   the   re- 

Find  remainders  : 

A 

5 

C 

D 

E 

F 

a.         88 

59 

78 

49 

76 

63 

-41 

-34 

15 

28 

-33 

-41 

&.         46 

55 

67 

88 

89 

54 

-15 

-  94 

.I/T: 

36 

75 

-46 

-32 

c.         79 

58 

62 

85 

93 

87 

-23 

-32 

31 

41 

-52 

-63 

d.        45 

86 

66 

67 

64 

77 

-44 

-21 

45 

33 

-22 

-32 

e.         56 

47 

83 

78 

99 

65 

-32 

-41 

32 

51 

-34 

-44 

/         63 

75 

96 

48 

84 

97 

-42 

-31 

43 

25 

-52 

-23 

Addition  and  Subtraction 

Sight 

Exercises 

A 

B            C 

D 

E 

F 

G 

a.       17 

21         21 

32 

37 

37 

20 

-1-4 

-4      -17 

+  5 

-32 

-5 

-6 

b.       12 

19         19 

11 

19 

19 

19 

+  7 

-7      -12 

4-8 

-8 

-11 

+  6 

INTRODUCTORY  REVIEW 


17 


Oral  Problems 

1.  If  John  spends  5  cents  out  of  a  dime,  how  much 
change  does  he  get  ? 

2.  There  were  14  pears  on  a  branch.     How  many 
were  there  after  Mary  picked  off  7  ? 

3.  A  boy  had  9  marbles.     How  many  had  he  after 
losing  4  of  them  ? 

4.  A  girl  is  8  years  old.     How  old  was  she  3  years 

ago? 

Oral  Drills 


The  sign  of  equality  is  = ,  called  equals. 


13  +  4=17  means  13  plus  4 
read  "  13  and  4  are  17." 

17  —  4  =  13  means  17  minus 
be  read  "  17  less  4  are  13." 

Give  answers : 


.     It  may  be 
13.     It  may 


A 

B 

c 

D 

a. 

14  +  4 

o 

18- 

14  =  ? 

418- 

4  =  ? 

24  +  4  =  ? 

b. 

13  +  6 

ft 

19- 

13  =  ? 

19- 

6  =  ? 

43  +  6  =  ? 

c. 

11  +  3 

A 

14- 

11  =  ? 

14- 

3  =  ? 

61  +  3  =  ? 

d. 

12  +  5 

=  ? 

17- 

12  =  ? 

17- 

5  =  ? 

32  +  5  =  ? 

e. 

15  +  2 

=  ? 

18- 

16  =  ? 

18- 

2  =  ? 

75  +  2  =  ? 

f. 

10  +  9 

=  ? 

19- 

10  =  ? 

19- 

9  =  ? 

50  +  9  =  ? 

ff- 

14  +  3 

=  ? 

17- 

14  =  ? 

17- 

3  =  ? 

84  +  3  =  ? 

A. 

16  +  2 

=  ? 

18- 

16  =  ? 

18- 

29 
—  . 

26  +  2  =  ? 

I 

12  +  7 

=  ? 

19- 

12  =  ? 

19- 

7  =  ? 

92  +  7  =  ? 

18  SECTION  ONE 

Addition  and  Subtraction 
Oral  Problems 

1.  In  an  orchard  there  are  1 1  trees  in  the  first  row 
and  10  trees  in  the  second.     How  many  are  there 
in  both  rows  ? 

2.  After  plowing  36  acres  how  many  acres  must 
Mr.  Jones  plow  to  finish  a  40-acre  field  ? 

3.  I  bought  goods  amounting  to  42  cents  and 
received  8  cents  in  change.     How  much  did  I  hand 
the  storekeeper  ? 

4.  A  girl  has  44  cents.     How  many  more  cents 
does  she  need  in  order  to  buy  a  50-cent  doll  ? 

5.  There  are  18  yards  of  cloth  in  one  roll  and  10 
yards  in  another.     How  many  yards  are  there  in  both 
rolls  ? 

6.  After  selling  22  dozen  eggs,  a  grocer  has  7 
dozen  left.     How  many  dozen  did  he  have  at  first  ? 

7.  Edward  has  24  marbles  and  Arthur  has  6  more 
than  Edward.     How  many  has  Arthur  ? 

^/s.   Sarah  has  26  cherries.     How  many  will  she 
have  if  she  gives  10  to  Jane  ? 

^.   Frank  is  16  years  old.     In  how  many  years 
will  he  be  21  ? 

10.  A  boy  picked  27  quarts  of  berries.     How  many 
quarts  will  he  have  after  selling  19  ? 

11.  Mr.  Jones  is  25  years  old.     How  old  was  he  9 
years  ago  ? 


INTRODUCTORY  REVIEW  19 

Written  Problems 

1.  In  an  orchard  there  are  26  trees  in  the  first 
row  and  31  trees  in  the  second  row.     How  many  are 
there  in  both  rows  ? 

2.  After  cutting  24  acres  of   wheat,  how  many 
more   acres  will  Mr.   Wise  have  to  cut  to  finish  a 
45-acre  field? 

3.  I  bought  goods   amounting  to   52  cents  and 
received  23  cents  in  change.     How  much  did  I  hand 
the  storekeeper? 

4.  A  boy  has  62  cents.     How  many  more  cents 
does  he  require  in  order  to  buy  a  75-cent  baseball  ? 

5.  There  are  23  yards  of  silk  in  one  roll  and  25 
yards  in  another.     How   many  yards   are   there   in 
both  rolls? 

6.  After  selling  22  dozen  eggs,  a  grocer  has  16 
dozen  left.     How  many  dozen  did  he  have  at  first  ? 

7.  Fred  has  24  marbles,  and  George  has  1 5  more 
than  Fred.     How  many  has  George  ? 

8.  Minnie  has  26  cherries.     How  many  will  she 
have  if  she  gives  13  to  her  brother  ? 

9.  Robert  is  11  years  old.     In  how  many  years 
will  he  be  27  ? 

10.  A   girl    picked   36    quarts   of    berries.      How 
many  quarts  will  she  have  after  selling  25  ? 

11.  Mr.  Smith  is  38  years  old.     How  old  was  he 
17  years  ago  ? 


20  SECTION  ONE 

Notation  and  Numeration 

One   hundred   is   written    100.     Two   hundred  is 
written  200.     Three  hundred,  300. 

1.  Write  in  figures   (a)  four   hundred.     (6)  Five 
hundred,      (c)    Six    hundred,      (d)    Seven    hundred. 

One  hundred  one  is  written  101. 

2.  Write  in  figures  (a)  one  hundred  three.    (&)  One 
hundred  four,     (c)  One  hundred  five,     (d)  One  hun- 
dred six.     (e)  One  hundred  seven. 

One  hundred   ten  is  written  110.     Two  hundred 
twenty-five  is  written  225. 

3.  Write  in  figures: 

a.  One  hundred  twenty.  Five  hundred  thirty-one. 
6.  Three  hundred  one.     Seven  hundred  eighty-four. 

4.  Read  the  following: 

a.    Ill  202  317  496  500 

6.    630  782  867  999  840 


In  writing  hundreds,  three  figures  are  used. 
The  right-hand  figure  is  called  the  ones'  figure,  the 
next  is  called  the  tens'  figure,  and  the  left-hand 
one  is  called  the  hundreds'  figure. 


5.    Write  in  figures: 

a.    One  hundred  ninety.       Five  hundred  twenty-two. 
6.    Two  hundred  seventy.  Six  hundred  seventy-three. 


INTRODUCTORY  REVIEW  21 

Adding  by  6's.    By  7's. 

1.  There  are  6  houses 
on  one  side  of  the  street 
and   6    houses   on   the 
other.     How   many 
houses    are    there     on 
both  sides? 

2.  How  many  are  6  and  6  ? 

3.  After  spending  7  cents,  a  girl  has  6  cents  left. 
How  many  cents  did  she  have  at  first  ? 

4.  How  many  are  6  and  7? 

5.  Charles  has  saved  8  cents.     He  needs  6  cents 
more  to  buy  a  book.     How  much  does  the  book  cost? 

6.  How  many  are  6  and  8  ? 

7.  If  I  pick  9  roses,  there  will  be  6  still  on  the 
bush.     How  many  are  there  on  the  bush? 

s.   How  many  are  6  and  9? 

9.    In  a  class  there  are  7  boys  and  7  girls.     How 
many  pupils  are  in  the  class? 

10.  How  many  are  7  and  7? 

11.  A  pole  was  cut  into  two  pieces,  one  8  feet  long 
and  the  other  7  feet  long.     How  long  was  the  pole 
at  first? 

12.  How  many  are  7  and  8  ? 

13.  After  giving  9  cherries  to  his  sister,  a  boy  has 
7  left.     How  many  cherries  had  he  ? 

14.  How  many  are  7  and  9  ? 


22  SECTION  ONE 

Adding  by  8's.    By  9's 

1.  How  many  pies  are  8  pies  and  8  pies  ? 

2.  There  are  9  cars  in  one  train  and  8  in  another. 
How  many  cars  are  there  in  both  ? 

3.  How  many  are  8  and  9  ? 

4.  In  a  game  of  ball  there  are  9  boys  on  one  side 
and  9  on  the  other.     How  many  are  there  on  both 
sides  ? 

Sight  Drills 


Give  sums  : 

A 

B 

c 

D 

E 

F 

G 

H 

a. 

6 

7 

8 

9 

7 

8 

9 

8 

6 

6 

6 

6 

7 

7 

7 

7 

&. 

6 

6 

6 

7 

7 

8 

9 

9 

7 

8 

9 

8 

9 

9 

8 

9 

Sight  Exercises 
Add  the  following : 

ABODE 

a.  20      25      20  25  20 

20      10       1L5  20  30 

6.  35      30      30  40  20 

10      15      20  20  40 

c.  15      40      15  25  15 

40      15      20  40  30 

d.  30      40      50  60  70 
30      40      50  60  70 


INTRODUCTORY  REVIEW  23 

Written  Exercises 

i.    A  rope  was  cut  into  three  pieces  42,  63,  and  24 
ft.  long.     What  was  the  length  of  the  original  rope  ? 


* 

PROCESS 

Begin  at  the  bottom. 
Think  7  (4  +  3),  9  ;  write  9.  Thii 
8  (2  +  6),  12  ;  write  12. 

42ft. 
63 
>k      24 

Ans.  129  ft. 

2.  Add: 

A 

B 

c 

D 

E 

a.  33 

40 

70 

92 

75 

20 

63 

80 

80 

3 

54 

25 

_3 

16 

61 

b.  64 

27 

33 

40 

3' 

14 

91 

4 

73 

93 

80 

_1 

81 

25 

_93 

c.  102 

122 

306 

5 

620 

203 

122 

50 

203 

113 

10 

122 

401 

30 

204 

d.  620 

90 

140 

30 

120 

61 

305 

200 

304 

302 

3 

402 

24 

43 

416 

e.  234 

82 

311 

232 

13 

40 

105 

25 

32 

143 

121 

12 

123 

232 

143 

24  SECTION  ONE 

Addition  with  Carrying 
3.   Add  53,  136,  78,  and  684. 


PROCESS 

Begin  with  the  ones'  column. 
Think  12  (4  +  8),  18,  21  ;  write  1  and 
carry  2.     Think   10  (2  +  8),   17,  20,  25  ;  * 
write  5  and  carry  2.     Think  8  (2  +  6),  9  ; 
write  9.                                                               Ans. 

53 
136 

78 
684 

951 

4.    Find  sums : 


a. 


c. 


d. 


e. 


A 

B 

C 

D 

E 

64 

20 

23 

16 

5 

33 

15 

64 

5 

23 

127 

357 

227 

117 

215 

26 

14 

7 

119 

8 

25 

2 

321 

103 

342 

140 

27 

33 

25 

32 

56 

18 

33 

15 

359 

4 

9 

234 

8 

80 

123 

234 

345 

456 

203 

47 

58 

207 

345 

88 

6 

9 

163 

20 

8 

449 

909 

175 

473 

219 

81 

44 

184 

250 

62 

314 

30 

400 

26 

105 

5 

16 

37 

105 

30 

INTRODUCTORY  REVIEW 

Testing  Results 
*.   Add  278,  166,  37,  and  69. 


25 


TEST 

After  obtaining  the  sum  by  adding  the  col- 
umns upward,  test  the  result  by  adding  the 

278 
166 

columns  downward,  thus:  14,  21, 

30;  10,16, 

37 

19,  25  ;  4,  5. 

69 

Ans 

.  550 

6.    Find  sums 

.     Test  : 

A 

B 

c 

D 

E 

.a.     35 

160 

313 

464 

7 

323 

48 

46 

203 

322 

150 

204 

65 

45 

48 

&.    106 

220 

27 

423 

152 

38 

417 

341 

240 

236 

23 

75 

35 

86 

324 

400 

130 

305 

100 

88 

c.   606 

108 

22 

40 

200 

70 

75 

123 

38 

106 

147 

6 

34 

50 

.   84 

1 

201 

5 

527 

40 

32 

2 

580 

44 

35 

d.   26  +  26  + 

26  +  26. 

h. 

34  +  605  +  21 

+  83. 

e.   45  +  45  + 

45  +  25. 

i. 

210  +  35  +  406  +  54. 

/.   34  +  26  + 

101  +  5. 

3- 

25  +  27  +  320 

+  105. 

g.   4  +  89  +  25  +  103. 

k. 

84  +  106  +  50 

+  19. 

26 


SECTION  ONE 
One  Half.     One  Quarter 


H 


< 


One  half  is  written  |.     One  quarter  is  written  J. 


Fold  circles,  squares,  etc.,  to  show  that  a  half  is  one  of  the 
two  equal  parts  of  a  thing,  and  that  a  quarter  is  one  of  its  four 
equal  parts. 

Oral  Examples 

1.  How  many  halves  in  a  pie  ? 
How  many  quarters? 

2.  If  a  boy  eats  one  quarter 
of  a  pie,  how  many  quarters  are 
left? 

3.  How   many  quarters   of   a 
pie  are  there  in  half  a  pie  ? 

4.  If  a  half  of  a  pie  costs  10 
cents,  what  is  the  cost  of  the  whole  pie  ? 

5.  Find  the  cost  of  a  quarter  of  a  pie  when  a  half 
pie  costs  10  cents. 

6.  When  milk  costs  6  cents  a  quart,  what  does  a 
pint  cost  ? 

7.  There  are  12  eggs  in  a  dozen ;  how  many  eggs 
are  there  in  a  dozen  and  a  half  ? 


INTRODUCTORY  REVIEW 
Roman  Numbers 


27 


Letters  are  sometimes  used  to  express  numbers, 

especially  in  clocks  and  watches,  also  in  chapters  of 
books,  etc. 

I  represents  1  VII  represents  7 

II  represents  2  VIII  represents  8 

III  represents  3  IX  represents  9 

IV  represents  4  X  represents  10 
V  represents  5  XI  represents  11 

VI  represents  6  XII  represents  12 

On  the  face  of  a  clock  IIII  is  used  to  represent  4. 

Telling  Time 

1.  If  the  minute  hand  goes  12  spaces  in  an  hour, 
how  many  spaces  does  it  go  in  one  half  hour  ? 

2.  What  time  is  it  when  the  minute  hand  points 
to  XII  and  the  hour  hand  to  IIII  ? 

3.  Tell  the  time  when  the  minute  hand  is  at  VI 
and  the  hour  hand  is  halfway  between  II  and  III. 

4.  When  it  is  a    quarter-past  six,  where   is   the 
minute  hand  ?     The  hour  hand  ? 

•    5.   When  it  is  a  quarter  to  one,  where  is  the  minute 
hand  ?     The  hour  hand  ? 

e.   What  is  J  of  12?    Jof  12? 


28  SECTION  ONE 

Addition  and  Subtraction 
Oral  Problems 

1.  A  man  had  50  bushels  of  tomatoes.     He  sold 
all  but  4  bushels.     How  many  bushels  did  he  sell  ? 

2.  A  girl  had  50  cents.     How  many  cents  had  she 
after  spending  41  cents  ? 

3.  A   cheese   weighed   45   pounds   and   the   box 
weighed   10  pounds.      How  many  pounds  did  both 
weigh  ? 

4.  A  boy  had  36  firecrackers  after  he  had  shot 
off  9.     How  many  had  he  at  first  ? 

5.  I  gave  the  grocer  75  cents  and  he  gave  me 
9  cents  change.     What  did  the  goods  cost? 

6.  A  telegraph  pole  is  24  feet  above  the  ground 
and  6  feet  in  the  ground.     How  long  is  the  pole  ? 

7.  There  are  15  flowers  on  one  bush  and  8  on 
another.     How  many  are  there  on  both  ? 

8.  How  many  days  are  there  from  December  15 
to  December  25? 

9.  A  farmer  has  42   sheep.      How   many  more 
must  he  buy  in  order  to  have  50  ? 

10.  Find   the   total   cost   of    28   cents'    worth   of 
cake  and  9  cents'  worth  of  candy. 

11.  One  day  a  boy  rode  to  a  town  25  miles  distant 
and  back  again.     How  far  did  he  ride  ? 


INTRODUCTORY  REVIEW 


29 


Written  Problems 

i/  A  man  had  75  bushels 
i  ofpotatoes.    He  used  21  bush- 
els and  sold  the  rest.     How 
many  bushels  did  he  sell  ? 

2.  A  boy   had    75    cents. 
How  many  cents  had  he  after 
spending  33  cents  ? 

3.  A    cheese    weighed    48 
pounds  and  the  box  weighed 
12  pounds.       What  was   the 
weight  of  both  ? 

4.  A  girl  had  36  cherries  after  giving  36  to  her 
brother.     How  many  did  she  have  at  first? 

5.  I  gave  the  baker  25  cents  and  he  gave  me 

11  cents  change.     What  did  the  goods  cost? 

6.  A  flag  pole  is  38  feet  above  the  ground  and 

12  feet  in  the  ground.     How  long  is  it  ? 

7.  There  are  37  roses  on  one  bush  and  29  on 
another.     How  many  are  there  on  both  ? 

8.  How  many  days  are  there  from  March  13  to 
March  29? 

9.  A  farmer  has  24  sheep.     How  many  does  he 
need  in  order  to  have  37  ? 

10.  What  is  the  total  cost  of  28  cents'  worth  of 
coffee  and  22  cents'  worth  of  sugar? 

11.  A  city  is  48  miles  away.      How  many  miles 
does  a  person  ride  in  going  and  returning  ? 


30 


SECTION  ONE 
Equal  Parts 


1.  Fold  a  paper  circle  into  two  equal  parts.     What 
is  each  part  called  ?     One  half  is  written  ^-. 

2.  Fold  a  paper  circle  into  four  equal  parts.    What 
is  each  part  called  ?     One  fourth  is  written  J. 

3.  Fold  a   paper   square   into   three   equal   parts. 
Each  part  is  called  one  third.    One  third  is  written  ^. 

4.  Fold  a  paper  square  into  six  equal  parts.     Each 
part  is  called  one  sixth.     One  sixth  is  written  J. 

5.  How  many  thirds  are   there  in  a   pie?     How 
many  sixths  ? 

6.  How  many  sixths  in  one  half  a  pie  ?     In  one 
third  of  a  pie  ? 

Quart  and  Peck 

NOTE.     The  pupil  should  discover  by  measuring  that  there 
are  8  quarts  in  a  peck. 

1.  How  many  quarts  are  there  in  a  peck  ? 

2.  Change  2  pecks  to  quarts. 

3.  Change  16  quarts  to  pecks. 

4.  If  I  feed  a  quart  of  grain  every  day  to  my 
chickens,  how  long  will  a  peck  last  ? 

5.  If  I  feed  them  2  quarts  of  grain  every  day  how 
long  will  a  peck  last  ? 


INTRODUCTORY   REVIEW  31 

Subtraction 
Written  Exercises 

1.  Find  the  difference  between  90  and  74. 

PROCESS 

90  Write  the  larger  number,  90,  above  the 

_  JA  smaller.     Begin  at  the  ones'  column. 

— —       .  Since  4  is  greater  than  0,  think  4  and  6 

(writing   6)  are  10.     Carry  1  to   7  which 
makes  8.     Think  8  and  1  (writing  1)  are  9. 

Test  by  adding  16  and  74  upward:    thinking  6  and  4, 
2  (carrying  1)  and  7. 

2.  Subtract.     Test : 

A                     B                    C                     D  E 

a.  31               46               92               84  63 

-19            -27            -79            -69  -48 

b.  50               92               83               30  63 
-25            -75            -26             -15  -35 

c.  63               92               84               72  50 
-24            -65             -15            -36  -26 

d.  61               66              90              81  60 
-19            -27            -19            -69  -15 

e.  81               76               56               70  82 
-29            -27            -28            -25  -36 

/.          93               75               82               61  54 

-46           -38           -26           -38  -27 


32  SECTION  ONE 

3.   Fron  318  take  276. 


PROCESS 

318  Think  6  and  2  (writing  2)  are  8.     Think 

27 f)  1  an^  4  (writing  4)  are  11.     Carry  1  to  2, 

which  makes  3.     As  this  is  the  same  as  the 
A*)     A^yis 

'  upper  number,  do  not  write  anything  under 

the  hundreds'  column. 


4.    Subtract : 

ABODE 

a.         239  327  479  569  648 

-156        -246        -382        -481        -560 


&. 

725 

878 

915 

879 

712 

c. 

-654 

-792 

-830 

-693 

-651 

625 

568 

449 

316 

229 

-571 

-475 

-365 

-294 

-195 

s.   Subtract 

92  from  500. 

PROCESS 

500 
-92 

Ans. 

Think  2  and 
1  to  9,  which 
(writing  0)  are 
(writing  4)  are 

8  (writing  8)  are  10. 
makes  10.     Think  10 
10.     Carry  1.     Think  1 
5. 

Carry 
and  0 
and  4 

408 

A 

B 

C 

D 

E 

a. 

900 

800 

700 

600 

500 

b. 

-75 

-63 

-37 

-44 

-88 

311 

311 

100 

100 

100 

-91 

-291 

-50 

-95 

-15 

INTRODUCTORY  REVIEW  33 

Review  Exercises  $ 


In  addition  and  in  subtraction  the  numbers  have  names, 
as  follows : 

'    Addition  Subtraction 

256     Addend  512     Minuend 

+  256     Addend  -256     Subtrahend 

Ans.       512     Sum  Ans.      256     Difference 


In   subtraction   the   difference    is   also  called    the 
remainder. 

• 

1.  Find  sums.     Test : 

a.    198  +  73  +  206  +  5  +  382. 
6.   46  +  514+103  +  8  +  29. 

c.  184  +  291  +  332  +  45  +  9. 

d.  55  +  326  +  84  +  173  +  270. 

e.  321  +  78  +  97  +  84  +  259. 

2.  Find  differences.     Test : 

a.  321-259.  6.  291-184.  c.  915-876. 

d.  840-326.  e.  665-486.  /.  824-632. 

g.  270-73.  h.  533-486.  i.  733-543. 

j.  514-29.  *.  910-707.  I  642-438. 

m.  382-206.  n.  623-341.  o.  551-275. 


34  SECTION  ONE 

Written  Problems 

1.  A   girl   has   58    cents.      She   needs    17   cents 
more  to  buy  a  doll.     What  is  the  price  of  the  doll  ? 

2.  A  farmer  raised  75  loads  of  hay.      He  used 

17  loads  and  sold  the  rest.     How  many  loads  did 
he  sell  ? 

3.  A  boy  had  75  cents.     How  much  had  he  after 
spending  50  cents? 

4.  When  a  boy  saves  16  cents  more,  he  can  buy 
a  75-cent  pair  of  gloves.     How  much  has  he  saved 
already  ? 

5.  How  much  older  is  a  man  50  years  old  than  his 
son  who  is  16  ? 

6.  How  many  days  from  May  14  to  Decoration 
Day,  May  30  ? 

7.  Mr.   Smith    is    18    years    younger    than   Mr. 
Brown,  who  is  41  years  old.     How  old  is  Mr.  Smith  ? 

8.  Jacob  caught   17  fish  and  Horace  caught  17 
more  than  Jacob.     How  many  did  Horace  catch  ? 

9.  Mrs.  Jones  is  27  years  old.     How  old  will  she 
be  16  years  from  now  ? 

10.  Mr.  Jones  is  36  years  old.     How  old  was  he 

18  years  ago  ? 

11.  A  girl  has  50  cents;  how  much  will  she  have 
if  she  spends  26  cents  ? 


SECTION   II 

Preliminary  Exercises 

1.  Add  the  following : 

123456789 
4-1  +2  +3  +  4  +5  +6  +7  +8  +9 

Instead  of  writing  1,  2,  3,  4,  etc.,  twice,  as  examples 
in  addition,  they  may  be  written  as  multiplication 
examples  thus : 

123456789 
x2  x2  x2  x2  x2  x2  x2  x2  x2 

These  are  read  2  times  1,  2  times  2,  2  times  3,  etc. 

2.  How   many   are    2    times     1  ?      2    times    2  ? 
2   times  3?     2  times  4?     2  times  5?     2  times  6? 
2  times  7?     2  times  8?     2  times  9? 


The  sign  of  multiplication  is   x  ,  called  times. 


3.    Find  the  cost  of  2  baseballs  at  5  cents  each. 
If   1   baseball  costs  5  cents  2  baseballs  will  cost 
2  times  5  cents.     Am.  10  cents. 


The  answer  in  multiplication  is  called  the  product. 

35 


36  SECTION  TWO 

Oral  Problems 

1.  How  many  feet  have  2  cows  ? 

2.  If  I  pay  9  cents  for  1  bat, 
how  much  must  I  pay  for  2  bats  ? 

3.  How  many  desks  are  there 
in  2  rows,  if  there  are  8  desks  in  each  row  ? 

*  4.    Mary  has  2  nickels.     How  many  cents  has  she  ? 

5^5.    A  boy  has  2   pockets  and  3  marbles  in  each. 
How  many  marbles  has  he  in  both  pockets  ? 

y-  6.   How  many  feet  have  2  birds  ? 

<i/7.    If  ribbon  cost  6  cents  a  yard,  how  many  cents 
will  2  yards  cost  ? 

8.   How  many  days  are  there  in  2  weeks  ? 

Blackboard  Exercises 

Give  orally  from  the  blackboard  or  the  book  the 
product  of  each  number  beginning  at  the  ones'  figure ; 
thus  2  times  0  are  0,  2  times  2  are  4 ;  etc. 


A 

B 

c 

D 

E 

F 

G 

a. 

20 

30 

40 

21 

31 

41 

22 

x2 

x2 

x2 

x2 

x2 

x2 

x2 

I. 

32 

42 

23 

33 

43 

24 

34 

x2 

x2 

x2 

x2 

x2 

x2 

x2 

MULTIPLICATION  37 

Written  Exercises 


A 

B 

c 

D 

E 

a. 

201 

211 

212 

221 

213 

x2 

x2 

x2 

x2 

x2 

&. 

232 

234 

243 

341 

324 

x2 

x2 

x2 

x2 

x2 

c.  Add  206  and  206. 

d.  Multiply  206  by  2. 


.206 
+  206 

PROCESS 

Think  2  times  6  are  12; 
write  2  and  carry  1.    Think 
ns.    2  times  0  are  0;  carrying  1 
makes    1;  write  1.     Think 
2  times  2  are  4  ;  write  4. 

206 

412   A 

412   Ans. 

e.   216 
x2 

250 
x2 

126 
x2 

345 

x2 

237 
x2 

/   450 
x2 

307 
x2 

208 
x2 

109 
x2 

245 
x2 

g.   356 
x2 

449 
x2 

380 
x2 

279 
x2 

165 
x2 

h.    259 
x2 

316 
x2 

478 
x2 

156 
x2 

209 
x2 

38  SECTION   TWO 

Review 

1.  How  many  are  2  +  2  +  2  ?     Three  2's  are  how 
many  ?     Two  3's  are  how  many  ? 

2.  How   many   are    2  +  2  +  2  +  2?     Four   2's   are 
how  many  ?     Two  4's  are  how  many  ? 

3.  How  many  are  2  +  2  +  2  +  2  +  2?      Five  2's  are 
how  many  ?     Two  5's  are  how  many  ? 

4.  How  many  are  six  2's  ?     Two  6's  ? 

5.  How  many  are  seven  2's  ?     Two  7's  ? 

6.  How  many  are  eight  2's  ?     Two  8's  ? 

7.  How  many  are  nine  2's  ?     Two  9's  ? 

Oral  Problems 

1.  What  is  the  cost  of  five  2-cent  postage  stamps  ? 

2.  How  many  legs  have  8  birds? 

3.  James  is  6   years  old ;  his  brother  is  twice  as 
old.     How  old  is  his  brother  ? 

4.  At  2  marbles  for  a  cent,  how  many  marbles  can 
I  buy  for  6  cents  ? 

5.  Find  the  cost  of  9  rockets  at  2  cents  each. 

6.  How  many  pints  are  there  in  4  quarts  ? 

7.  How  many'  cents  are  there  in  2  dimes  ? 

8.  If  a  family  uses  2  quarts  of  milk  a  day,  how 
many  quarts  will  be  used  in  a  week  ? 

9.  How  many  shoes  in  nine  pairs  ? 


MULTIPLICATION  39 

Memorize  the  Following  Tables 

Two  times  1  are  2  One  time  2  is  2 

Two  times  2  are  4  Two  times  2  are  4 

Two  times  3  are  6  Three  times  2  are  6 

Two  times  4  are  8  Four  times  2  are  8 

Two  times  5  are  10  Five  times  2  are  10 

Two  times  6  are  12  Six  times  2  are  12 

Two  times  7  are  14  Seven  times  2  are  14 

Two  times  8  are  16  Eight  times  2  are  16 

Two  times  9  are  18  Nine  times  2  are  18 

Written  Exercises 
Multiply : 


A 

B 

C 

D 

E 

a.      20 

22 

21 

20 

21 

x3 

x4 

x5 

x6 

x  7 

b.      20 

21 

22 

12 

21 

x5 

x6 

x7 
102 

x8 

x9 

c.    102 

102 

102 

102 

x3 

x4 

x5 

x6 

x7 

d.    102 

102 

112 

112 

112 

x8 

x9 

x5 

x7 

x6 

e.    122 

122 

122 

122 

122 

x6 

x7 

x5 

x4 

x3 

40  SECTION  TWO 

Dividing  by  2 
Preliminary  Exercises 

1.  How  many  2's  are  there  (a)  in  4  ?      (b)  In  2  ? 
(c)  In    8?      (d)  In   0?      (e)    In    16?     (/)  In    10? 
(g)  In  12?     (A)  In  14?     (i)  In  6?     (j)  In  18? 

These  examples  may  be  written  thus : 

(a)  2)4  (6)  2)2  (c)  2)8  (d)  2)0  (e)  2)16 

?  ?  ?  ?  ? 

(/)  2)10  (?)  2)12  (A)  2)14  (i)  2)6  (./)  2J18 

?  ?  ?  ?  ? 

2.  Give  answers. 

Oral   Problems 

1.  How  many  2-cent  postage  stamps  can  I  buy  for 
10  cents  ? 

2.  William  is  12  years  old.     He  is  twice  as  old  as 
his  brother.     How  old  is  his  brother  ? 

3.  How  many  2-cent  rockets  can  be  bought  for  18 
cents  ? 

4.  If  2  marbles  cost  1  cent,  how  many  cents  will 
12  marbles  cost? 

5.  How  many  quarts  are  there  in  8  pints  ? 

6.  In  16  shoes  how  many  pairs  ? 

Sight  Exercises 
A  B  C  D  E  F 

a.  2)44        2)48        2)42       2)46        2)60        2)66 

b.  2)64        2)68        2)62       2)80        2)84        2)88 


DIVISION  41 


Written  Exercises 
i.    Divide  608  by  2. 


PKOCESS 


Begin  at  the  hundreds'  figure.    Think  2      2)608 
into  6  (goes)  3  times,  and  write  3  directly         "304"  A.HS 
under  the  6 ;  think  2  into  0  (goes)  0  times, 
and  write  0  directly  under  the  0 ;  think  2  into  8  (goes)  4 
times,  and  write  4  directly  under  the  8. 


2.  Divide : 

A  B  C  D 

a.  2)264  2)668  2)482  2)864 

I.   3)360  3)666  4)484  4)888 

3.  Divide  186  by  2. 


Since  1  does  not  contain  2,  think  2  into  18      2)186 
(goes)  9  times,  write  9  under  the  8,  etc. 


A  B  C  D 

a.   2)126  2)148  2)160  2)184 

6.   5)105  6)126  7)147  8)168 

4.   Divide  778  by  2. 


Say  2  into  7  (goes)  3  times  and  1  over ;  2  2^778 

into  17  (goes)  8  times  and  1  over ;  2  into  18 
(goes)  9  times.  Ans'  389 


42  SECTION  TWO 

5.    Find  quotients : 


a. 

A 

2)376 

B 
2)532 

C 

2)792 

D 

2)942 

b. 

2)110 

2)276 

2)830 

2)706 

c. 

2)310 

2)216 

2)912 

2)138 

6. 

Divide  : 

a. 

A 
3)363 

B 

5)510 

(7 

7)784 

D 

3)606 

b. 

5)610 

7)854 

3)366 

5)605 

c. 
d. 

8)896 
4)880 

4)884 

6)612 

9)108 

8)816 
9)918 

6)732 

7.  What  is  J  of  52  ? 

i  of  52  =  26  Ans.     Divide  52  by  2. 

8.  Give  answers  : 

a.  i  of  72.  c.   i  of  30.  e.   \  of  56. 

b.  I  of  36.  d.   1  of  54.  /.   1  of  70. 
cj.   What  is  1  of  88? 

\  of  88  =  22  Ans.     Divide  88  by  4. 


a.  1  of  840.          d.   1  of  488.          g.   J  of  804. 

b.  J  of  480.  e.   1  of  840.          h.   1  of  484. 

c.  1  of  800.          /   1  of  408.  I   l  0/844. 


REVIEWS  43 

Oral  Problems 

1.  What  is  the  cost  of  \  pound  of  20-cent  coffee  ? 

2.  A  boy  has  15  packs  of  firecrackers.    How  many 
packs  will  he  have  after  he  has  shot  off  5  packs  ? 

3.  There  are  14  boys  and  11  girls  in  a  class.     How 
many  pupils  are  there  in  the  class  ? 

4.  A  man  has  62  apple  trees  and  53  peach  trees. 
How  many  more  apple  trees  has  he  than  peach  trees  ? 

5.  In  a  class  of  24  pupils  the  number  of  boys  and 
of  girls  is  the  same.     How  many  are  there  of  each  ? 

6.  How  many  oranges  are  2  dozen  oranges? 

7.  How  many  ears  of  corn  are  there  on  9  stalks  if 
there  are  2  ears  on  each  stalk  ? 

Written  Problems 

1.  What  is  the  cost  of  \  yard  of  70-cent  silk  ? 

2.  A   man   has    50    packs   of   firecrackers      How 
many  will  he  have  after  he  sells  15  packs? 

3.  There   are  24  boys  and  26  girls  in  the  park. 
How  many  children  are  there  in  the  park  ? 

4.  A   man  has  62  apple  trees  and  26  peach  trees. 
How  many  more  apple  trees  has  he  than  peach  trees  ? 

5.  There  are  60  trees  in  5  equal  rows.     How  many 
trees  are  there  in  each  row  ? 

6.  How  many  oranges  are  7  dozen  oranges? 

7.  F?w  many  ears  of  corn  are  there  on  19  stalks  if 
there  are  2  on  each  stalk  ? 


44  SECTION  TWO 

Multiplying  by  3 
Preliminary  Exercises 

1.  Add  the  following : 

345  6789 
345  6789 
_3  4  5  6789 

24 

2.  Copy  the  following,  and  fill  the  blanks.     Learn 

the  table. 

3  times  1  are — .  3  times  4  are — .  3  times  7  are — . 
3  times  2  are — .  3  times  5  are — .  3  times  8  are — . 
3  times  3  are — .  3  times  6  are — .  3  times  9  are — . 

Blackboard  Exercises 
Give  products : 


A 

B 

c 

D 

E 

F 

a. 

30 

40 

50 

60 

70 

80 

x3 

x3 

x  3 

x3 

x3 

x3 

b. 

90 

81 

72 

63 

52 

41 

x3 

x3 

x3 

x  3 

x3 

x3 

Written  Exercises 


Multiply  : 

A 

B 

C 

D 

E 

a. 

104 

205 

306 

207 

308 

x3 

x3 

x3 

x3 

x  3 

b. 

139 

228 

317 

246 

154 

x  3 

x3 

x3 

x3 

x3 

DIVISION  45 


Dividing  by 

3 

Blackboard  Exercises 

A 

B 

c 

D 

a.     3)270 

3)180 

3)690 

3)219 

6.     3)120 

3)150 

3)156 

3)390 

c.     3)240 

3)210 

3)123 

3)696 

Written  Exercises 

Divide  : 

A 

B 

c 

D 

a.     3)372 
b.     3)459 
c.     3)675 

3)117 
3)288 
3)135 

3)945 

3)876 
3)798 

3)402 

3)504 
3)7^)5 

d.     3)750 

3)258 

3)621 

3)801 

e.     3)543 

3)177 

3)510 

3)948 

Multiplication  and 

Division 

Find  answers  : 

A 

B 

C 

D 

a.      233  x 

4         103  x  9 

123x4 

132x6 

6.      4)928 

9)927 

mbmm^ffm 

4)532 

6)798 

c.      123  x 

5         113x8 

132x5 

131  x6 

d.      5)665 

8)984 

5)515 

7)791 

e.      123  x 

7         123x6 

103x8 

113x5 

46  SECTION  TWO 

Oral  Problems 

1.  If  there  are  8  desks  in  a  row,  how  many  desks 
are  there  in  3  rows  ? 

2.  A   boy  has  20  cherries.     How  many  will  he 
have  after  he  gives  3  away  ? 

3.  At  3  for  a  cent  what  will  be  the  cost  of  15 
marbles  ? 

4.  After  selling  17  quarts  of  milk  a  man  has  3 
quarts  left ;  how  many  quarts  had  he  at  first  ? 

5.  What  does  a  man  gain  if  he  buys  a  cow  for  $27 
and  sells  it  for' $30? 

6.  Find  the  cost  of  3  pounds  of  sugar  at  6  cents 
a  pound. 

7.  At  2  cents  a  mile  how  far  can  I  ride  in  a  train 
for  20  cents? 

8.  A  girl  buys  21  cents'  worth  of  bread.     She  gives 
the  baker  25  cents.     How  much  change  does  he  give 
her  ? 

9.  How  many  days  are  there  from  December  21  to 
December  25  ? 

10.  At  3  cents  each,  how  many  pads  can  be  bought 
for  15  cents  ? 

11.  Four  years  ago  a  boy  was  seven.     How  old  is 
he  now  ? 

12.  How  many  weeks  are  there  in  21  days  ? 


REVIEWS  47 

Written   Problems 

1.  If  there  are  15  desks  in  a  row  how  many  desks 
are  there  in  3  rows  ? 

2.  A  boy   has   31  marbles.     How  many  will  he 
have  if  he  gives  12  away? 

3.  At  3  for  a  cent  what  will  be  the  cost  of  45 
marbles  ? 

4.  After  selling  17  quarts  of  milk  a  man  has  23 
quarts  left;  how  many  quarts  had  he  at  first? 

5.  What  does  a  man  gain  if  he  buys  a  cow  for  $27 
and  sells  it  for  $41? 

6.  Find  the  cost  of  3  pounds  of  lard  at  15  cents  a 
pound. 

7.  At  2  cents  a  mile  how  far  can  I  ride  in  a  train 
for  92  cents? 

8.  A  girl  buys  21  cents'  worth  of  bread.     She  gives 
the  baker  50  cents.     How  much  change  does  he  give 
her? 

9.  How   many   days  are  there  from  June  13  to 
June  30? 

10.  At  3  cents  each  how  many  pads  can  be  bought 
for  45  cents? 

11.  Fourteen  years  ago  a  man  was  26.     How  old 
is  he  now? 

12.  How  many  weeks  are  there  in  91  days? 


48  SECTION  TWO 

Multiplying  by  4 

1.  Count  by  4's  to  40. 

2.  Copy  the  following  and  fill  the  blanks.     Learn 
the  table. 

4  times  1  are — .  4  times  4  are — .  4  times  7  are — . 
4  times  2  are — .  4  times  5  are — .  4  times  8  are — . 
4  times  3  are — .  4  times  6  are — .  4  times  9  are —  . 

3.    Multiply:  - 


A 

B 

c 

~r\ 

E 

a. 

14 

24 

34 

44 

234 

x  4 

x  4 

x  4 

x  4 

x  4 

I. 

25 

35 

45 

55 

245 

x  4 

x  4 

x  4 

x  4 

x4 

c. 

36 

46 

56 

66 

156 

x  4 

x  4 

x  4 

x  4 

x  4 

d. 

47 

57 

67 

77 

167 

x  4 

x  4 

x4 

x4 

x  4 

e. 

58 

68 

78 

88 

188 

x  4 

x  4 

x  4 

x  4 

x  4 

f 

69 

79 

89 

99 

199 

x  4 

x  4 

x  4 

x  4 

x  4 

DIVISION 

49 

Divide. 

Dividing  by 

4 

A 

a.   4)456 

" 

6.   4)936 
c.   4)580 

B 

4)496 



4)976 
4)620 

C 

4)536 

4)500 
4)980 

D 

4)476 

4)540 
4)544 

d.   4)584 

4)624 

4)664 

4)984 

e.   4)668 
/.   4)712 

4)708 
.  4)672 

4)628 

4)700 

4)632 

4)752 

g.   4)760 

4)796 

4)788 

4)780 

Multiplication  and 
Find  answers  : 

Division 

A 

a.   144x5 

B 

144x6 

C 
134x7 

D 

124x8 

6.    5)720 

6)804 

7)868 

8)912 

c.    104x9 

123x8 

124x7 

134x5 

d.  9)936 

8)992 

7)798 

5)670 

e.   114x6 

114x7 

114x8 

103x9 

/   6)204 

7)308 

8)272 

9)396 

50  SECTION  TWO 

Oral  Problems 

1.  "When  \  pound  of  candy  costs  10  cents,  what  is 
the  cost  of  a  pound? 

2.  When  there  are  8  desks  in  each  row,  how  many 
desks  are  there  in  4  rows  ? 

3.  A  woman  had  40  chickens ;  how  many  had  she 
after  selling  32  ? 

4.  Find  the  cost  of  ^  yard  of  linen  at  28  cents  per 
yard. 

5.  At  4  for  a  dollar,  how  many  dollars  would  16 
baseballs  cost  ? 

6.  At  4  yards  for  a  dollar,  how  many  yards  can 
be  bought  for  $  5  ? 

7.  A   boy   earned    50   cents.     He   spent   all   but 
7  cents.     How  much  did  he  spend  ? 

8.  If  a  man  saves  $  8  each  month,  how  much  does 
he  save  in  4  months  ? 

9.  A  farmer  bought  a  cow  for  $  36  and  sold  it  for 
$  4  more.     How  much  did  he  get  for  it  ? 

10.  A  girl  divides  a  number  by  4  and  her  answer 
is  8.     What  is  the  number  ? 

11.  A  farmer  had  42  sheep.     How  many  would  he 
have  if  he  bought  8  more  ? 

12.  If  4  boys  take  4  days  to  do  a  piece  of  work, 
how  long  would  it  take  1  boy  to  do  it  ? 


REVIEWS  51 

Written  Problems 

1.  When  \  pound  of  candy  costs  16  cents,  what 
is  the  cost  of  a  pound  ? 

2.  When  there  are   13  desks  in  each  row,  how 
many  desks  are  there  in  4  rows  ? 

3.  A  woman  had  40  chickens ;  how  many  had  she 
after  selling  28  ? 

4.  Find  the  cost  of  \  yard  of  silk  at  56  cents  per 
yard. 

5.  At  4  for  a  dollar,  how  many  dollars  would  60 
baseballs  cost  ? 

6.  At  4  yards  for  a  dollar,  how  many  yards  could 
be  bought  for  $  12  ? 

7.  A  boy  earned  50  cents.     He  spent  all  but  27 
cents.     How  much  did  he  spend  ? 

8.  If  a  man  saves  $  15  each  month,  how  much  does 
he  save  in  4  months  ? 

9.  A  man  bought  a  cow  for  $  36  and  sold  it  for 
$  14  more.     How  much  did  he  get  for  it  ? 

10.  A  girl  divides  a  number  by  4  and  her  answer 
is  16.     What  is  the  number  ? 

11.  A  farmer  has  42  sheep.     How  many  would  he 
have  if  he  bought  18  more  ? 

12.  If  4  men  take  16  days  to  do  a  piece  of  work, 
how  long  would  it  take  1  man  to  do  it  ? 


52 


Multiplying  by  5 

1.  Count  by  5's  to  100. 

2.  Copy  the  following  and  fill  the  blanks.     Learn 
the  table : 

5  times  1  are  — .  5  times  4  are  — .  5  times  7  are  — . 
5  times  2  are  — .  5  times  5  are  — .  5  times  8  are  — . 
5  times  3  are  — .  5  times  6  are  — .  5  times  9  are  — . 

3.  Multiply : 


A 

B 

C 

D 

E 

a. 

15 

25 

35 

45 

55 

x5 

x5 

x5 

•    x5 

x5 

b. 

26 

36 

46 

56 

66 

x5 

x5 

x  5 

x5 

x5 

c. 

37 

47 

57 

67 

77 

x5 

x5 

x5 

x  5 

x5 

d. 

48 

58 

68 

78 

88 

x5 

x5 

x5 

x5 

x5 

e. 

59 

69 

79 

89 

99 

x5 

x5 

x5 

x5 

x5 

ft 

155 

135 

105 

105 

115 

x6 

x7 

x8 

x9 

x8 

9- 

125 

145 

123 

123 

55 

x7 

x6 

x7 

x8 

x  9 

DIVISION  53 

Dividing  by  5 
Divide : 

A                           B  C  D 

a.  5)625  .            5)675  5)725  5)775 

b.  5)680              5)730  5)780  5)830 

c.  5)735            (  5)785  5)835  5)885 

d.  5)790              5)840  5)890  5)940 

e.  5)845              5)895  5)945  5)995 
/    6)930              7)875  8)920  9)945 
g.   6)330              7)315  8)280  9)225 

Examples  in  division  are  written  in  several  ways : 


Divisor  3) 30  Dividend.      Dividend  30      -,A    ^     ,. 

<!——  — -  =  10    Quotient. 

Ans.     10  Quotient.       Divisor      3 

Dividend  Divisor  Quotient 

30  -5-  3  =  10 


Sight  Exercises 


Give  answers  : 

A 

B 

C 

D 

a.  36  +  8 

21  +  7 

50-46 

Jof  32 

6.  32  +  8 

32-4 

5x9 

18  +  7 

c.  4  x  4 

£of  12 

27  +  3 

25-18 

d.  32-28 

44  +  6 

iof  12 

24  +  8 

e.  \  of  16 

9x5 

35  +  7 

55-9 

64 


SECTION  TWO 
Pint,  Quart,  Gallon 


1  Pint 


1  Quart 


1  Gallon 


1.  How  many  times  will  the  gallon  measure  hold 
the  contents  of  the  quart  measure  ? 

2.  How  many  quarts  are  there  in  a  gallon  ? 

3.  How  many  pints  are  there  in  a  gallon  ? 

4.  How  many  quarts  of  milk  are  there  in  a  can 
of  milk  containing  10  gallons  ? 

5.  When  a  half  pint  of  ice  cream  costs  10  cents, 
what  is  the  cost  of  a  pint  ? 

6.  How  many  pints  are  there  in  2  quarts  and  1 
pint? 

7.  How  many  quarts  are  there  in  3  gallons  ? 

8.  How  many  gallons  are  there  in  16  quarts? 

9.  How  many  pints  are  there  in  2  gallons  ? 
10.    Learn  the  following  table : 

Liquid  Measure 
TABLE 

2  pints  (pt.)      1  quart  (qt.) 
4  quarts  1  gallon  (gal.) 

Liquid  measure  is  used  in  buying  and  selling  liquids ; 
such  as  milk,  oil,  sirup,  etc.,  also  ice  cream. 


MEASUREMENTS 


55 


Rectangles 

1.  Make  a  one-inch  cardboard  square.     This  con- 
tains 1  square  inch. 

2.  Draw  a  rectangle  2  inches  long,  1  inch  wide. 
Divide  it  into  one-inch  squares.     How  many  square 
inches  does  it  contain  ? 


3.  Arrange  6  one-inch  squares  to  form  a  rectangle 
3  inches  long,  2  inches  wide.     What  part  of  the  whole 
rectangle  is  the  rectangle  formed  by  a  horizontal  row 
of  3  squares  ?     What  part  of  the  whole  rectangle  is 
the  rectangle  formed  by  a  vertical  row  of  2  squares  ? 
What  part  of  the  whole  rectangle  is  each  square  ? 

4.  What  part  of  6  square  inches  is  1  square  inch  ? 
What  part  of  6  is  3  ?     What  part  of  6  is  2  ? 

Inch  is  written  in.-,  foot  is  written /£.;  square  inch 
is  written  sq.  in. 


56  SECTION  TWO 

Oral  Problems 

1.  If  I  pay  5  cents  for  a  quarter  of  a  pound  of 
candy,  what  is  the  price  of  a  pound  ? 

2.  There  are  16  ounces  in  a  pound.     How  many 
ounces  are  there  in  a  quarter  of  a  pound  ? 

3.  If  a  man  uses  28  quarts  of  oil  in  a  year,  how 
many  gallons  does  he  use  ? 

4.  At  4  cents  per  quart,  what  is  the  cost  of  a 
gallon  of  oil  ?     )  d> 

s.    John  has  36  cherries,  James  has  4  more  than 
John.     How  many  has  James  ? 

6.  A  farmer  has  40  cows.     How  many  will  he 
have  if  he  sells  4  ? 

7.  How  many  sheep  at  $  4  each  can  be  bought 
for  $  36  ? 

8.  What  will  4  yards  of  9-cent  calico  cost  ? 

9.  There   are   36   trees  in  4  equal  rows.     How 
many  are  there  in  each  row  ? 

10.  If   one  quarter  pound  of   tea  costs   10  cents, 
what  is  the  cost  of  one  half  pound? 

11.  How  many  tomato  plants  will  be  needed  for 
9  rows  if  10  plants  are  needed  for  each  row  ? 

12.  How  many  nickels  make  20  cents  ? 

13.  A  girl  has  in  her  bank  a  quarter,  a  dime,  and 
a  nickel.     How  many  cents  are  there  in  her  bank  ? 

14.  How  many  pints  of  milk  will  make  12  half- 
pint  glasses  of  milk  ? 


REVIEWS  57 

Written  Problems 

1.  If  I  pay  15  cents  for  a  quarter  of  a  pound  of 
tea,  what  is  the  price  of  a  pound  ? 

2.  There  are  144  pens  in  a  gross.     How  many 
pens  are  there  in  a  quarter  of  a  gross  ? 

3.  How  many  gallons  are  there  in  100  quarts  ? 

4.  At  18  cents  per  quart,  what  will  a  gallon  of 
paint  cost  ? 

5.  Thomas  has  36  cents ;  Martha  has  24   cents 
more  than  Thomas.     How  much  money  has.  Martha  ? 

6.  A  farmer  has  60  sheep.     How  many  will  he 
have  if  he  sells  36  ? 

7.  How  many  sheep  at  $4  each  can  be  bought 
for  $  64  ? 

8.  What  is  the  cost  of  4  yards  of  dress  goods  at 
16  cents  a  yard  ? 

9.  There   are   96   trees  in  4  equal  rows.     How 
many  are  there  in  each  row  ? 

10.  If  one  quarter  yard  of  silk  costs  36  cents,  what 
is  the  cost  of  one  half  yard  ? 

11.  How  many  cabbage  plants  are  required  for  4 
rows  if  there  are  23  plants  in  each  row  ? 

12.  How  many  nickels  make  70  cents  ? 

13.  How  much  money  are  a  half  dollar,  a  quarter, 
a  dime,  a  nickel,  and  6  cents  ? 

14.  How  many  pints  of  lemonade  will  make  36 
half-pint  glasses  of  lemonade  ? 


58 


SECTION  TWO 


Time 

60  seconds  (sec.)  1  minute  (min.) 

60  minutes  1  hour  (hr.) 

24  hours  1  day  (da.) 

7  days  1  week  (wk.) 

1.  How  many  minutes  in  ^ 
hour? 

2.  The  minute   hand   takes 
5  minutes  to  go  from  XII  to  I. 
How  many  minutes  does  it  take 
to  go  from  XII  to  VI  ? 

3.  "When  the  minute  hand  is 
at  I,  it  is  5  minutes  after  the 

hour.     How  many  minutes  is  it  after  the  hour  when 
the  minute  hand  points  to  V  ?    To  II  ?     To  III  ? 

4.  When  the  minute  hand  is  at  VII  it  is  25  minutes 
to  the  next  hour.     How  many  minutes  to  the  next 
hour  is  it  when  the  minute  hand  points  to  IX  ?     To 
XI?     To  VIII?     ToX? 

5.  Where  is  the  minute  hand  at  10  minutes  after 
3  ?     At  20  minutes  to  5  ? 

6.  What  part  of  an  hour  space  does  the  hour  hand 
go  in  30  minutes?     In  15  minutes?    In  20  minutes? 
In  10  minutes  ? 

Roman  Numbers 

13        14       15       16         17          18         19       20 
XIII    XIV    XV    XVI    XVII    XVIII    XIX    XX 


NUMBERS  OF  FOUR  FIGURES  59 

Notation  and  Numeration 

1.  One  thousand  is  written  1,000.     Two  thousand 
is  written  2,000. 

2.  Read:  3,000;  5,000;  7,000;  9,000. 

3.  Write  in  figures :  four  thousand ;  six  thousand ; 
eight  thousand. 

4.  One  thousand  one  is  written  1,001.     Two  thou- 
sand six  is  written  2,006.     Three  thousand  twenty  is 
written  3,020.     Six  thousand  five  hundred  thirty-six 
is  written  6,536. 

5.  Write  in  figures :  four  thousand  three  hundred 
seventy-four ;    six   thousand   seven    hundred ;    eight 
thousand   ninety ;    one   thousand   sixty-two ;    seven 
thousand  eight;   two  thousand  five;   nine  thousand 
five  hundred  ninety ;  one  thousand  three ;  five  thou- 
sand seventy-five ;  three  thousand  six  hundred  seventy- 
three. 

6.  Read  the  following  numbers : 

A  B  C  D 

1,834  9,703  8,046  3,000 

4,039  5,000  3,604  4,500 

607  750  707  2,908 

6,300  2,030  98  5,660 

8,270  572  2,345  789 

509  1,111  670  1,050 

1,062  7,008  2,010  9,590 

7.  Find  the  sum  of  each  column. 


60  SECTION  TWO 

8.  Write  in  figures : 

Six  hundred  ninety-nine. 

Eight  hundred  five. 

Three  thousand  seven  hundred  thirty-eight. 

Nine  thousand  eight  hundred  four. 

Two  thousand  seven  hundred  twenty-six. 

Seven  thousand. 

9.  Add  the  foregoing. 

10.    Write  the  following,  and  add : 

Three  thousand  sixty-four. 

Seven  hundred  nineteen. 

Eighty-two. 

Five  hundred  sixty. 

Two  thousand  three  hundred  five. 

Four  hundred. 


In  a  number  of  four  figures  the  right-hand  fig- 
ure is  called  the  ones'  figure,  the  next  is  called  the 
tens'  figure,  the  next  is  called  the  hundreds'  figure, 
and  the  left-hand  figure  is  called  the  thousands' 
figure. 


A  comma  is  generally  used  to  separate  the  thou- 
sands' figure  from  the  hundreds'  figure,  except  in 
numbers  representing  dates,  such  as  Jan.  1,  1914. 

Numbers  of  four  figures  are  frequently  read  as  hun- 
dreds :  1,800  being  read  as  eighteen  hundred;  1,912, 
as  nineteen  hundred  twelve. 


ROMAN  NUMBERS 


61 


Roman  Numbers 

20  is  written  XX.  60  is  written  LX. 

30  is  written  XXX.  70  is  written  LXX. 

40  is  written  XL.  80  is  written  LXXX. 

50  is  written  L.  90  is  written  XC 

100  is  written  C. 

A  number  between  20  and  29,  30  and  39,  40  and 
49,  etc.,  is  expressed  by  placing  the  letter  or  letters 
representing  the  ones  after  the  letter  or  letters  repre- 
senting the  tens. 


28  is  written  XXVIII. 
34  is  written  XXXIV. 
49  is  written  XLIX. 
63  is  written  LXIII. 


57  is  written  LVII. 
72  is  written  LXXII. 
96  is  written  XCVI. 
85  is  written  LXXXV. 


Express  in  Roman  numbers : 

ABODE 

22  66  82  49  18 

33  77  75  31  27 

44  88  64  26  32 

55  99  59  81  46 


Read  : 

A 

B 

c 

D 

XXIII 

XLVIII 

LXVI 

XLV 

XXIV 

LXVII 

XXV 

LXIX 

LVII 

XXXVI 

XLII 

XXXV 

XLIX 

XCIX 

XXIX 

XLVII 

NOTE.     Owing  to  their  limited  application,  but  little  attention 
should  be  given  to  Roman  numbers. 


62  SECTION  TWO 

Dollars  and  Cents 

Twenty-three  dollars  five  cents  is  written  $  23.05. 
A  period,  called  a  decimal  point,  is  placed  before 
the  cents. 

Read  the  following : 

A  B  c  D 

$4.76  $1.25  $43.55  $805.07 

$9.83  $3.75  $27.09  $914.30 

Write : 

1.  Five  dollars  and  seventy-nine  cents. 

2.  Eight  dollars  and  sixty-four  cents. 

3.  Forty-two  dollars  and  eight  cents. 

4.  Sixty  dollars  and  sixty  cents. 
Seventy-five  cents  is  written  $  .75. 

Sometimes  a  cipher  is  written  before  the  decimal  point, 
seventy-five  cents  being  written  $  0.75 ;  and  two  ciphers  may 
be  written  after  the  decimal  point  when  there  are  no  cents, 
twenty-seven  dollars  being  written  $  27.00. 

Read  the  following: 

ABODE 

$.84  $0.16  $.47  $0.05  $.15 

$.09  $0.25  $.63  $0.13  $.94 

Write: 

1.  Four  cents.     Twenty  cents.  Twenty-six  cents. 

2.  Ten  cents.      Fifty  cents.      Eighty-five  cents. 

3.  Three  cents.    Sixty  cents.      Ninety-nine  cents. 

4.  Seven  cents.  Eleven  cents.   Seventy-three  cents. 


FEDERAL  MONEY  63 

Sight  Exercises 


Give 
a. 

b. 
c. 
d. 
e. 

f- 

ff- 

h. 

i. 
j- 

answers  : 

A 

$1.50 

+  .25 

B 

$0.38 
+  0.40 

$0.30 
+  0.30 

c 

$.60 
+  .35 

D 

$3.47 
+  1.20 

$2.40 
+  2.40 

$.50 
+  .80 

$5.60 
+  1.15 

$2.40 
x2 

$0.30 
x3 

$.20 
x4 

$1.10 
x5 

$1.50 
-.25 

$1.00 
-.05 

$0.40 
+  .38 

$.75 
-.45 

$3.47 
-1.20 

$2.00 
-.10 

$.50 
-.25 

$4.00 
-.30 

$2.40 
+  .60 

$3.50 
-3.25 

$.60 
+  .50 

$4.00 
+  3.70 

$4.80 

$0.60 

$.80 

$4.40 

2 

$1.50 
x2 

3 

$0.25 
x4 

40 

$.50 
x3 

4 

$1.12 
x4 

$3.00 
2 

$2.50 
+  .60 

$1.00 

$.66 

$1.60 

5 

$2.50 
-.60 

22 

$.60 
+  .45 

4 

$1.60 
-.45 

64  SECTION  TWO 

Addition 

Written  Exercises 

i.   A  grocer  paid  out  the  following  amounts :  $2.84, 
$0.47,  $0.09,  $16.56,  $3.25.     How  much  did  he  pay? 


$2.84 
Arrange  the  numbers  so  that  the  deci-  ._ 

mal  points  will  be  in  the  same  column, 

OQ 
then  add.     Place  a  decimal  point  in  the  <uy 

result  under  the  other  decimal  points.  16.56 

Prefix  the  dollar  mark  to  the  first  addend  3.25 

and  to  the  sum.  An^  $23.21 


2.  Find  the  sum  of  $  50.75,  $  18.94,  $  7.80,  $  6.66, 
and  $10.95. 


PROCESS 

Adding  upward,  the  totals  of  the  columns  are : 
1st  column,  11  (ignore  0),  15,  20  (write  0). 
2d  column,  (carrying  2),  11, 17,  25,34, 41  (write  1). 
3d  column,  (carrying  4  and  ignoring  0),  10,  17,  «  50.75 
25  (ignoring  0)  (write  5).  18  94 

4th  column,  (carrying  2),  3,  4,  9  (write  9). 

7.80 

TEST  ggg 

To  test  the  result,  cover  it,  and  add  downward.          1095 
Adding  downward,  the  totals  are : 


<J>    Q  (•     -I  f\ 

1st  column,  9,  (ignoring  0),  15,  20  (write  0). 
2d  column,  (carrying  2),  9, 18,  26,  32,  41  (write  1). 
3d  column,  (carrying  4  and  ignoring  0),  12,  19, 
25  (ignoring  0)  (write  5). 
4th  column,  7,  8,  9  (write  9). 


ADDITION  65 

3.    Add  and  test : 

a.    $49.62       b.    $.12.13  c.    $36.81       d.      $4.23 

6.38                 8.75  .66  51.75 

4.79               24.30  3.75  9.67 

.24                 3.98  .10  .82 

.07                   .70  20.99  9.56 


e. 

$40.09 

/      $0.98 

g.      $15.18 

h.      $  1.43 

27.59 

62.44 

7.29 

77.48 

1.35 

4.85 

38.54 

4.69 

6.47 

9.00 

.85 

5.40 

.36 

.84 

8.00 

.41 

i. 

$9.10 

j.    $48.57 

k.     $8.88 

I    $56.89 

7.45 

4.84 

17.77 

9.99 

45.85 

6.95 

9.00 

.48 

27.58 

5.63 

6.38 

7.21 

6.24 

17.77 

37.36 

20.75 

m.    $  21.27  +  $  7.54  +  $  5.68  +  $  17.85  +  $  0.97. 
n.    $  26.79  +  $  2.15  +  $  7.17  +  $  0.98  +  $  12.49. 

4.  Find  the  sum  of  three  dollars  nineteen  cents, 
forty-three   dollars   eight   cents,    seven   dollars,  five 
dollars,  five   dollars   seventy-three   cents,  and  eight 
cents. 

5.  Add  nine  dollars  ninety-nine  cents,  forty-eight 
dollars  sixty-seven  cents,  eighty-eight  cents,  seventy- 
five  cents,  and  nineteen  dollars  nine  cents. 


66  SECTION  TWO 

Subtraction 
Written  Exercises 


To  test  the  result,  cover  the  minuend  and       $  40.33 
then  add   the   remainder   to  the    subtrahend,      _957Q 

adding  upwards :     4  +  9 ;  (carrying   1)    6  +  7 ;        

(carrying  1)  5  +  5;    (carrying  1)  2  +  2.     This       $  14.54 
sum  should  be  the  same  as  the  minuend  covered. 


1.  Find  remainders : 

A  B 

a.  $18.01 -$9.43  $27.44- $19.39 

6.  $48.63 -$8.77  $82.19- $78.90 

c.  $90.50 -$9.86  $35.04 -$16.66 

d.  $35.52 -$5.83  $63.15- $35.87 

e.  $53.60 -$8.75  $70.06- $42.19 

2.  From  ninety  dollars  take  ninety  cents. 

3.  Find     the    difference    between     sixty    dollars 
sixteen  cents  and  forty-three  dollars  three  cents. 

4.  From  the  sum  of  $3.50  and  $2.40  take  the 
difference  between  $7.50  and  $6.20. 

5.  From    $10    take   the    sum    of    $3.30,  $2.60, 
and  $1.50. 

6.  How  many  times  can  15  cents  be  subtracted 
from  75  cents? 

7.  How  many  times  must  25  cents  be  increased  by 
15  cents  to  make  a  total  of  70  cents  ? 


REVIEWS  67 

Sight  Drills 
1.    Add: 

A            B             C            D  E            F            G 

a.       50         40         20         40  32         20        14 

+  30     +50     +70     +20  +30     +42     +80 


I. 

60 

61 

43 

54 

63 

47 

58 

+  24     +24 

+  22 

+  25 

+  36 

+  20 

+  31 

2. 

Subtract 

. 

a. 

80 

80 

62 

62 

•  90 

94 

96 

-50      - 

-30 

-40 

-22 

-70 

-60 

-36 

b. 

84 

95 

84 

95 

76 

67 

59 

-53     - 

-72 

-31 

-23 

-30 

-44 

-29 

3. 

Multiply 

. 

a. 

40 

30 

20 

41 

32 

21 

11 

x2 

x3 

x4 

x2 

x3 

x4 

x9 

5. 

12 

13 

14 

22 

23 

24 

33 

x4 

x3 

x2 

x4 

x3 

x2 

x3 

c. 

20 

30 

40 

50 

60 

70 

80 

x9 

x8 

x7 

x6 

x5 

x4 

x3 

4. 

Divide  : 

a. 

80 

80 

60 

60 

60 

60 

60 

2 

40 

20 

30 

2 

3 

10 

b. 

90 

90 

84 

84 

84 

96 

88 

30 

3 

42 

21 

4 

3 

4 

68  SECTION  TWO 

Oral  Problems 
i.    How  many  nickels  are  there  in  a  half  dollar  ? 


SOLUTION 

The  number  of  nickels  in  50  cents  is  the  number  of 
times  5  cents  is  contained  in  50  cents,  which  is  10.  Ans. 
10  nickels. 


2.    How  many  quarts  in  5  gallons? 


SOLUTIOX 


Since  there  are  4  quarts  in  1  gallon,  in  5  gallons  there 
are  5  times  4  quarts,  or  20  quarts.     Ans.   20  quarts. 


3.  Change  4  feet  to  inches. 

4.  Change  32  pecks  to  bushels. 

5.  At  5  cents  per  pound,  how  many  pounds   of 
sugar  can  be  bought  for  45  cents  ? 

6.  If  a  train  goes  45  miles  in  one  hour,  and  40  miles 
the  next  hour,  how  many  miles  does  it  go  in  two 
hours  ? 

7.  A  girl  is  taking  a  90-mile  trip  in  an  automobile. 
How  many  miles  has  she  yet  to  go  after  having  traveled 
60  miles  ? 

8.  How   many   pounds   of    5-cent    sugar    can   be 
bought  for  a  quarter   dollar  ?     A  half  dollar  ? 


REVIEWS  69 

Written  Problems 
i.   How  many  nickels  are  there  in  85  cents? 


SOLUTION 


To    find    the  number   of   5-cent  5  cents)  85  cents 
pieces  in  85  cents,  divide  85  cents       AnsTvi  (nickels) 
by  5  cents,  which,  gives  17.     The 
answer  is  17  nickels. 


2.   How  many  quarts  in  23  gallons? 


SOLUTION 


Since  1  gallon  is  equal  to  4  quarts,  23  gal-  4  qt. 

Ions  are  23  times  4  quarts,  or  92  quarts.  x  03 

NOTE.      Although  23  is  written  as  the     An«     <v>  nf 
multiplier,  the  product  is  obtained  by  mul- 
tiplying the   larger    number,   23,   by   the 
smaller  number,  4. 


3.  Change  7  feet  to  inches. 

4.  Change  96  pecks  to  bushels. 

5.  At  5  cents  per  pound,  how  many  pounds  can  I 
buy  for  95  cents? 

6.  If  a  boat  sails  47  miles  in  the  morning,  and  45 
miles  in  the  afternoon,  how  far  has  it  sailed  ? 

7.  A  boy  is  taking  a  90-mile  trip.      How  many 
miles  has  he  to  go  after  he  has  gone  47  miles  ? 

a.   How  many  pounds  of  5-cent  sugar  can  be  bought 
for  a  dollar  and  a  quarter  ? 


70 


SECTION  TWO 
Multiplication  Table 


1 

2 

3 

4 

5 

6 

7 

8 

9 

2 

4 

6 

8 

10 

12 

14 

16 

3 

6 

9 

12 

15 

18 

21 

4 

8 

12 

16 

20 

24 

5 

10 

15 

20 

25 

6 

12 

18 

24 

7 

14 

21 

8 

16 

9 

\ 

Copy  the  foregoing  table,  and  fill  the  vacant  spaces. 

Write  2  times  9  in  the  second  row  and  9  times  2  in  the 
second  column,  3  times  8  and  3  times  9  in  the  third  row,  8 
times  3  and  9  times  3  in  the  third  column,  etc. 

Oral  Exercises 

1.  Count  by  6's  to  60.       3.   Count  by  8's  to  80. 

2.  Count  by  7's  to  70.       4.   Count  by  9's  to  90. 

5.  How   many  are    (a)    six  6's  ?    (6)   Seven  6's  ? 
(c)  Eight  6's  ?  (d)  Nine  6's  ? 

6.  How  many  are  (a)  Seven  7's  ?    (6)  Eight  7's  ? 
(c)  Nine  7's? 

7.  How  many  are  (a)  eight  8's  ?    (&)  Nine  8's  ? 

8.  How  many  are  nine  9's  ? 


REVIEWS  71 

Oral  Problems 

1.  A  farmer  has  65  tons  of  hay.     How  many 
tons  will  he  have  after  selling  43  tons  ? 

2.  I  paid  84  cents  for  4  pounds  of  coffee.     What 
was  the  price  per  pound  ? 

3.  How  many  cars  are  there  in  two  freight  trains, 
one  having  32  cars  and  the  other  having  30  cars  ? 

4.  What  is  the  cost  of  3  yards  of  ribbon  at  32 
cents  per  yard  ? 

5.'  After  giving  away  one  half  of  his  firecrackers, 
Tom  has  42  left.     How  many  did  he  have  at  first  ? 

6.  When  tea  is  60  cents  a  pound,  what  part  of  a 
pound  can  I  buy  for  30  cents  ? 

7.  What  part  of  a  girl's  dollar  is  left  after  she 
spends  25  cents  ? 

8.  How  many  trees  are  there  in  4  rows  each  con- 
taining 22  trees  ? 

9.  How  many  pints  are  there  in  44  quarts  ?     How 
many  gallons? 

10.  How  many  feet  in  48  inches  ? 

11.  A  boy  gave  his  sister  12  cents,  which  was  one 
half  of  his  money.     How  many  cents  had  he  left  ? 

12.  A  man  is  37  years  old.     In  how  many  years 
will  he  be  40  ? 

is.   How  many  days  are  there  in  November  and 
December  ? 

14.   How  many  days  are  there  in  6  weeks  ? 


72  SECTION  TWO 

Multiplying  by  6 

Drill  Exercises 
Give  products : 


6x6 

7x6 

8x6 

9x6 

6x7 

7x5 

8x5 

9x5 

6x8 

7x4 

8x4 

9x4 

6x9 

7x3 

8x3 

9x3 

Written  Exercises 

i.   Multiply 

• 

A 

B 

c 

D 

E 

a.   666 

777 

888 

999 

666 

x6 

x6 

x6 

x6 

x7 

I.    666 

666 

678 

456 

567 

x8 

x9 

x6 

x6 

x6 

c.    345 

789 

456 

345 

234 

x6 

x6 

x8 

x8 

x9 

d.   345 

264 

360 

299 

647 

x7 

x6 

x6 

x6 

x6 

2.    Multiply  by  6  : 

A 

B 

c 

D 

E 

a.   344           1 

,448 

1,454 

1,583 

1,628 

&.   676           1,056 

1,536 

1,295 

1,468 

c.   458          1 

,374 

1,665 

1,378 

1,357 

d.  597          1 

,570 

1,498 

1,467 

1,555 

DIVISION  73 

Dividing  by  6 

Drill  Exercises 
Give  quotients : 

ABODE 

a.  6)36  6)42  8)32  7)42  6)30 

b.  8)40  7)35  9)54  8)48-  7)21 

c.  9)36  6)48  8)24  7)14  8)16 

d.  6)54  7)28  9)18  9)27  9)45 

e.  5)45  6)24  5)30  4)24  5)20 
/.  4)32  5)35  6)12  3)24  4)32 

Written  Exercises 

i.   If  one  tent  shelters  6  soldiers,  how  many  tents 
will  be  required  to  shelter  5,436  soldiers  ? 

When  the  first  quotient  figure  is  written  in 
its  proper  place,  each  remaining  figure  in  the    WO4ou  tents 
dividend  must  have  a  figure  in  the  quotient.  Alls.  906  tents 


DIVISION    TEST 

6)6,120         6)4,806  6)6,024 

Quotient       1,020  Ans.      801  Ans.      1,004  Ans. 
Divisor            x  6                x  6  x  6 

Dividend      6,120  4,806  6,024 

To  test  the  result,  cover  the  dividend  with  a  piece  of 
paper  and  write  on  the  latter  the  product  of  the  quotient 
by  the  divisor  without  rewriting  the  latter. 


74  SECTION  TWO 

Written  Exercises 
Divide.     Test  answers: 

ABC 

a.   6)1,056          6)1,572          6)2,286 


D 

6)2,160 


I.   6)2,670  6)3,966          6)3,588          6)2,370 


c.   6)4,068  6)4,416          6)5,244          6)5,658 


d.   6)6,816          6)6,432          6)6,468          6)7,344 


e.   6)7,740          6)8,670          6)8,832          6)8,634 


/   6)9,360  6)9,546          6)8,910          6)5,040 


g.  6)2,358          6)3,456          6)4,560          6)6,780 


h    6)7,890          6)8,910          6)9,870          6)8,766 


i.   6)3,996          7)1,638          8)2,600          9)2,376 


j.   6)4,662  7)2,345          8)1,800          9)4,995 


k.   6)5,328          7)2,268          8)1,888          9)3,996 


DIVISION  75 

Remainders  in  Division 
Sight  Exercises 

1.  If  I  desire  to  divide  7  apples  between  2  boys, 
how  many  whole  apples  can  I  give  each  ?     How  can 
I  divide  the  remaining  apple  between  them?     What 
is  each  part  called  ? 

2.  What  is  the  quotient  of  7  -*•  2  ? 


When  the  dividend  does  not  contain  the  divisor 
an  exact  number  of  times,  write  the  remainder,  then 
draw  a  line,  and  underneath  write  the  divisor. 

2)9  3)20  4)23 

Ans.  4^-        Am.     6f        Ans.     5f 


ARC 

a.   £=?  J^-=?  *£.=  ! 

I.    15-^2=?  19-3  =  ?  21-4=? 
3.    Give  answers : 

A                 B  C                D  E                F 

a.   3}22         8)41  6)37        9)25  5)51        6)51 

&.   2)25         3)38  4)51         8)25  7)51        6)25 

•                            n  '            •                           {.     i .     i  7          —                         ' 


A 

B 

c 

D 

a. 

£of  9 

JoflO 

iof  13 

Jof  31 

b. 

Jofll 

iof  13 

|of  15 

|of  52 

c. 

Jof  25 

£of  19 

jof  37 

Jof  52 

d. 

Jof  22 

Jof  25 

J  of  45 

^of  38 

76  SECTION  TWO 

Oral  Problems 

1.  How  many  hours  are  there  in  a  day  and  a  half  ? 

2.  A  farmer  had  80  acres  of  land.     He  sold  30 
acres.     How  many  acres  were  left  ? 

3.  If  one  man  takes  60  days  to  do  a  piece  of  work, 
how  long  would  it  take  3  men  to  do  it  ? 

4.  What  is  the  cost  of  40  newspapers  at  ^  cent 
each? 

5.  There  are  36  pupils  in  one  room  and  20  in  an- 
other.    How  many  are  there  in  both  rooms  ? 

6.  How  many  cars  in  3  trains,  each  containing 
20  cars  ? 

7.  How  many  weeks  are  there  in  35  days  ? 

8.  A  girl  is  8  years  old  and  her  mother  is   32 
years  old.     What  is  the  difference  in  their  ages  ? 

9.  How  many  books  are  on  two  shelves  one  con- 
taining 16  books  and.  the  other  containing  12  books  ? 

10.  How  many  ounces  in  a  pound  and  a  quarter  ? 

11.  How  many  minutes  in  3  hours  ? 

12.  How  many  horses  can  be  shod  with  24  shoes  ? 

is.  Three  feet  make  1  yard.  If  a  rail  is  10  yards 
long,  how  many  feet  long  is  it  ? 

14.  Two  boys  together  weigh  150  pounds.  If  one 
weighs  80  pounds,  what  is  the  weight  of  the  other  ? 

is.    How  many  months  are  there  in  three  years  ? 
is.    How  many  inches  in  2  feet  ? 


REVIEWS  77 

Written  Problems 

1.  How  many  hours  are  there  in  4  days  ? 

2.  A  farmer  has  80  acres  of  land.     How  much 
land  would  he  have  if  he  sold  36  acres  ? 

3.  If  one  man  takes  65  days  to  do  a  piece  of  work, 
how  long  would  it  take  5  men  to  do  it  ? 

4.  Find  the  cost  of  96  newspapers  at  ^  cent  each. 

5.  Mr.  Jones  has  36  pupils  in  his  class  and  Mr. 
Brown  has  38  pupils.     How  many  in  both  classes  ? 

6.  How  many  cars  in  4  trains  each  containing  24 
cars? 

7.  How  many  weeks  are  there  in  98  days  ? 

s.   A  boy  is  18  years  old   and  his  father  is   46 
years  old.     What  is  the  difference  in  their  ages  ? 

9.    There  are  26  books  on  one  shelf  and  24  on 
another.     How  many  books  are  there  on  both  shelves  ? 

10.  How  many  ounces  are  there  in  5  pounds  ? 

11.  How  many  minutes  are  there  in  9  hours  ? 

12.  How  many  horses  can  be  shod  with  96  shoes  ? 

13.  If  a  fence   is  16  yards  long,  how  many  feet 
long  is  it  ? 

14.  Two  boys  weigh  together  150  pounds.     If  one 
weighs  83  pounds,  what  is  the  weight  of  the  other  ? 

is.    How  many  mq|^hs  are  there  in  8  years  ? 
16.   How  many  inchl?  in  5  feet  ? 


78  SECTION  TWO 


a. 

7x7 

8x5 

9x5 

b. 

7x8 

8x6 

9x6 

c. 

7x9 

8x7 

9x7 

Written 

Exercises 

i. 

Multiply 

• 

A 

B 

C 

a. 

777 

888 

999 

x7 

x7 

x7 

b. 

777 

567 

765 

x9 

x7 

x7 

c. 

876 

789 

987 

x7 

*1 

x7 

d. 

878 

567 

765 

x7 

x8 

x8 

e. 

657 

576 

576 

x9 

x8 

x9 

2. 

Multiply 

by  7: 

A 

B 

C 

a. 

434 

1,234 

1,265 

b. 

766 

1,067 

1,347 

c. 

854 

1,285 

1,409 

Multiplying  by  7 

Drill  Exercises 

BCD 

8x4 
7x5 
7x6 


D 

111 

x_8 

678 
x7 

897 
x7 

657 
x8 

756 

x8 


D 

1,394 
1,406 
1,389 


MULTIPLICATION  AND  DIVISION 

Dividing  by  7 
Written  Exercises 
i.   Divide  and  test : 


79 


A 

5 

c 

D    - 

a.   7)1,057 

7)1,554 

7)2,261 

7)2,394 

b.   7)2,660 

7)2,156 

7)3,493 

7)2,835 

c.   7)4,361 

7)8,099 

7)5,075 

7)3,059 

d.   7)6,048 

7)4,263 

7)2,569 

7)9,982' 

e.   7)3,920 

7)7,329 

7)9,156 

7)7,049 

/  7)2,583 

7)7,098 

7)9,212 

7)4,760 

2.   Divide  by  7. 

Test: 

a.    9,842 

8,953 

9,569 

8,638 

6.   3,038 

9,863 

7,469 

9,723 

c.   8,932 

6,699 

5,978 

8,995 

Multiplication 

and  Division 

i.   Multiply  by 

7: 

A 

B 

C 

D 

a.   957 

1,380 

1,368 

1,278 

6.   826 

1,279 

1,276 

1,367 

2.   Divide  by  7. 

Test: 

a.    9,576 

8,946 

9,660 

9,758 

6.    5,782 

5,362 

8,855 

9,429 

80 


SECTION  TWO 


Oral  Problems 

1.  A  man's   farm   is   divided   into  4  fields,  each 
containing  8  acres.     How  many  acres  are  there  in  the 
farm  ? 

2.  If  8  panes  of  glass  are  required  for  each  window, 
how  many  windows  will  require  48  panes  ? 

3.  If   a   man  works   8   hours   a  day,  how  many 
hours  does  he  work  in  10  days  ? 

4.  In  an  orchard  of  80  trees  all  but  20  are  peach 
trees.    How  many  peach  trees  are  there  in  the  orchard  ? 

s.  How  many  players  are  needed  in  2  games  of 
football  if  each  game  requires  22  players  ? 

6.  A  boy  requires  12  days  to  do  one  fourth  of  a 
piece  of  work.  How  many  days  does  he  require  to  do 
the  whole  work  ? 


1915     JANUARY    1915 

Sun. 

Mon 

Tue. 

Wed. 

Thu. 

K-i. 

Sat. 

1 

2. 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

IS 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

2>lfi 

25 

26 

27 

28 

29 

30 

1915      FEBRUARY      1915 

Sun. 

Mon. 

Tue. 

Wed. 

Thu. 

Fri. 

Sat. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

15 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

7.  How   many   days   are   there   in   January   and 
February,  1915? 

8.  How  many  yards  of  wire  are  needed  to  make  a 
fence  20  yards  long,  if  the  fence  is  4  wires  high  ? 

9.  How   many    chestnuts   in    10  burs   containing 
2  nuts  each  and  10  containing  3  nuts  each  ? 


REVIEWS 


81 


Written  Problems 

1.  A  man  has  a  farm  consisting  of  7  fields,  each 
containing  14  acres.     How  many  acres  are  there  in 
the  farm? 

2.  If  8  panes  of  glass  are  required  for  each  win- 
dow, how  many  windows  will  require  96  panes  ? 

3.  If  a  farmer  works  13  hours  a  day,  how  many 
hours  does  he  work  in  7  days  ? 

4.  In  an  orchard  of  80  trees  all  but  28  are  apple 
trees.     How  many  are  apple  trees  ? 

5.  How  many  players  are  there   in  4  games  of 
baseball,  if  each  game  has  18  players  ? 

6.  A  man  requires  28  hours  to  do  one  third  of  a 
piece  of  work.     How  many  hours  does  he  require  to 
do  the  whole  work  ? 


1916    FEBRUARY    1916 

Sun. 

Mon. 

Tue. 

Wed. 

Thu. 

Fri. 

Sat. 

1 

2 

5 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

1916      MARCH      1916 

Sun. 

Mon. 

Tue. 

Wed. 

Thur 

Fri. 

Sat. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

15 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

2b 

27 

28 

29 

30 

31 

7.  How  many   days   are   there  in   February   and 
March,  1916? 

8.  How  many  yards  of  wire  are  required  to  make 
a  fence  27  yards  long  if  the  fence  is  3  wires  high  ? 

9.  How  many  chestnuts  in  26  burs  containing  2 
chestnuts  each  and  13  containing  3  chestnuts  each  ? 


}  SECTION  TWO 

Multiplying  by  8.    By  9 

Written  Exercises 
i.   Find  products : 

ABC 


a. 

888x8 

999x8 

888x9 

987x8 

I. 

887x8 

787x9 

887x9 

878x9 

c. 

678x8 

789x8 

897x8 

678x9 

d. 

788x8 

788x9 

878x8 

787x9 

e. 

999x9 

989x9 

899x9 

998x9 

/ 

567x8 

467x9 

576x8 

576x9 

2. 

Multiply  by 

8: 

A 

B 

c 

D 

a. 

1,056 

1,167 

1,234 

963 

I. 

1,067 

1,178 

1,245 

954 

c. 

1,088 

1,189 

1,225 

947 

d. 

1,079 

1,198 

1,229 

986 

e. 

1,097 

1,187 

1,239 

927 

/ 

1,099 

1,188 

1,236 

976 

3. 

Multiply  by 

9: 

A 

B 

C 

D 

a. 

1,023 

1,078 

1,099 

929 

6. 

1,034 

1,089 

1,088 

938 

c. 

1,045 

1,093 

1,077 

947 

rf. 

1,056 

1,095 

1,066 

956 

e. 

1,067 

1,097 

1,055 

965 

/. 

1,079 

1,068 

1,044 

987 

</. 

1,084 

1,072 

1,033 

976 

DIVISION 

Division  by  8.     By  9 

Written  Exercises 
i.   Divide  by  8.     Test: 


83 


A 

a.   8)3,752 

B 

8)8,520 

C 

8)9,984 

D 

8)8,352 

b.   8)7,144 

8)6,792 

8)7,776 
8)8,464 
8)6,976 
8)8,952 

8)6,384 
8)9,856 
8)8,224 
8)8,600 

c.   8)8,368 
d.   8)4,784 

8)8,744 

8)9,960 

e.   8)9,160 

8)5,536 

2.   Divide  by  9. 

A 

Test: 

B 

c 

D 

a.   9)7,317 

9)4,797 

9)6,804 

9)9,819 

I.   9)8,235 

9)6,669 

9)8,487 
9)5,166 
9)8,262 

9)9,450 

c.   9)6,489 

9)8,514 
9)6,957 

9)7,389 
9)5,517 

d.   9)6,507 

e.   9)5,625 

9)8,919 

9)5,328 

9)9,828 

3.   Find  quotients: 

A                               R 

a.   5)9,375            7)8,008 

c 

9)9,405 

D 

6)7,602 
5)8,425 
7)5,005 

b.   6)8,316 

8)9,512 

8)8,608 

c.   7)9,009 

9)8,838 

7)6,006 

84  SECTION  TWO 

Two  Operations 
Oral  Problems 

1.  If  2   bats   cost   20   cents,  what   will   be  the 
cost  of  1  bat  ?     What  will  be  the  cost  of  7  bats  ? 

2.  If  3  pounds  of  sugar  cost  18  cents,  what  will  5 
pounds  cost? 

3.  A  inan  gives  6  cherries  each  to  8  children. 
How  many  does  he  give  them  ?   If  he  had  50  cherries 
at  first,  how  many  would  be  left  ? 

4.  Mrs.  Smith  has  a  dozen  peaches.     How  many 
will  she  have  if  she  gives  2  to  each  of  her  3  children  ? 

5.  A  girl  buys  a  book  for  15  cents  and  a  writing 
pad  for  6  cents.     What  is  the  cost  of  both  ?     If  she 
hands  the  storekeeper   a   25-cent   piece,  how   much 
change  should  she  receive  ? 

6.  A  row  of  corn  contains  10  hills,  3  stalks  to  a 
hill.     How  many  stalks  are  there  in  the  row  ?     How 
many  stalks  are  there  in  2  rows  ? 

7.  John  has  2  pockets,  each  containing  9  marbles. 
How  many  marbles  has  he?     What  did  they  cost  at 
6  for  a  cent  ? 

8.  At  6  for  a  cent  what  will  be  the  cost  of  3  bags 
of  marbles  each  containing  8  marbles? 

9.  A   man   has  2   dozen    oranges.     How    many 
will  he  have  after  selling  5  oranges  ? 

10.  A  boy  has  40  cents.  How  much  would  he 
have  after  spending  25  cents  for  a  ball  and  10  cents 
for  a  bat  ? 


TWO  OPERATIONS  85 

11.  A  boy  set  out  3  rows  of  cabbage,  each  contain- 
ing 8  plants.     How  many  plants  did  he  set  out  ?     If 
he  set  out  6  plants  in  another  row,  how  many  plants 
did  he  set  out  all  together  ? 

12.  A  farmer  planted  5  rows  of  bea-ns,  10  hills  to  the 
row.     How  many  hills  did  he  plant  ?     If  he  planted 
14  hills  in  another  row,  how  many  hills  did  he  plant 
in  the  6  rows  ? 

13.  What  is  the  cost  of  one  half  of  a  20-cent  pie  ? 
What  is  the  cost  of  half  the  pie  and  25  cents'  worth 
of  sugar  ? 

14.  After  buying  \  pound  of  40-cent  tea,  a  girl  gets 
30    cents    change.     How    much   did    she   give   the 
grocer  ? 

is.  How  many  pints  of  milk  are  there  in  two  cans, 
one  containing  20  quarts  and  the  other  containing 
10  quarts? 

16.  A  man  had  20  quarts  of  berries.     He  used  12 
quarts  and  sold  the  remainder  for  5  cents  per  quart. 
What  did  he  get  for  those  he  sold  ? 

17.  A  lady  gave  a  half  dollar  and  3  dimes  for  2 
37ards  of  goods.     What  was  the  price  per  yard  ? 

is.  A  girl  rides  2  hours  in  a  train  going  40  miles 
per  hour,  and  3  hours  in  a  stage  going  3  miles  per 
hour.  How  far  does  she  go? 

19.  A  boy  is  reading  a  book  of  90  pages.  He  has 
read  40  pages.  How  long  will  it  take  him  to  com- 
plete the  book  if  he  reads  10  pages  an  hour  ? 


86  SECTION  TWO 

Written  Problems 

1.  If  2  bats  cost  30  cents,  what  will  be  the  cost  of 
1  bat  ?     What  will  be  the  cost  of  5  bats  ? 

2.  If  3  pounds  of  cheese  cost  48  cents,  what  will 
5  pounds  cost  ? 

3.  A  man  gives  16  cherries  apiece  to  4  children. 
How  many  does  he  give  them  ?     If  he  had  75  cherries 
at  first,  how  many  would  be  left  ? 

4.  Mr.  Smith  has  90  postage  stamps.     How  many 
will  he  have  after  giving  a  dozen  to  each  of  6  boys  ? 

5.  What   is  the  cost   of   a   35-cent  book  and   a 
16-cent   pad?     How   much   change   does   the  store- 
keeper give  out  of  75  cents  to  a  boy  who  buys  these 
two  articles  ? 

6.  A  row  of  corn  contains  16  hills,  3  stalks  to  a 
hill. .    How  many  stalks  are  there  in  the  row  ?     How 
many  stalks  are  there  in  2  rows  ? 

7.  William    has  3    boxes,   each    containing   25 
marbles.     How  many  marbles  has  he  ?     What  would 
they  cost  at  5  for  a  cent? 

8.  At  6  for  a  cent  what  would  be  the  cost  of  3 
boxes  of  marbles,  32  marbles  to  a  box  ? 

9.  A  man  has  6  dozen  lemons.    How  many  lemons 
has  he  ?         How  many  will  he  have  after  selling  25 
lemons  ? 

10.  A  girl  has  80  cents.  How  much  would  she 
have  after  spending  33  cents  for  a  doll  and  26  cents 
for  the  doll's  clothes  ? 


TWO  OPERATIONS  87 

11.  A  girl  planted  3  rows  of  geraniums,  14  plants 
in  a  row.     How  many  geraniums  did  she  plant  ?     If 
she  planted  18  pansies  also,  how  many  flowers  of  both 
kinds  did  she  plant  ? 

12.  Ida  had  3  cards  of  buttons,  each  containing  24 
buttons,  and  one  card  containing  18  buttons.     How 
many  buttons  were  there  in  the  4  cards  ? 

is.  Find  the  cost  of  \  pound  of  tea  costing  70 
cents  per  pound.  Find  the  total  cost  of  the  tea  and 
a  pound  of  25-cent  coffee. 

14.  After  buying  \  pound  of  60-cent  tea  a  boy 
gets  35  cents  in  change.  How  much  did  he  give  the 
storekeeper  ? 

is.  How  many  quarts  of  milk  are  there  in  two 
cans,  one  containing  9  gallons  and  the  other  contain- 
ing 7  gallons  ? 

16.  A  girl  gathered  40  quarts  of  berries.     She  pre- 
served 34  quarts  and  sold  the  remainder  for  16  cents 
per   quart.     What  did   she   get   for  those  she  sold  ? 

17.  A  lady   gave  3  quarters  and  3  nickels  for  6 
yards   of    muslin.     What   did   the   muslin   cost   per 
yard? 

is.  A  boy  rode  2  hours  on  a  train  going  38  miles 
per  hour  and  3  hours  in  a  stage  going  4  miles  per 
hour.  How  far  did  he  ride  ? 

19.  A  girl  is  reading  a  book  of  123  pages.  She  has 
read  68  pages.  How  long  will  it  take  her  to  com- 
plete the  book  if  she  reads  eleven  pages  an  hour  ? 


88  SECTION  TWO 

Multiplying  by  10 
Sight  Exercises 

1.  How   many  cents  in  2  dimes?     In   3    dimes? 
In  5  dimes?     In  9  dimes?     In  10  dimes? 

2.  How  many  are  ten  2's?     Ten  4's?     Ten  6's? 


To  multiply  a  number  by  10  affix  a  cipher  to  the 
multiplicand. 

Thus  16  x  10  =  160  ;           25  x  10  =  250. 

3.    Give  products  : 

ABC 

a.    17x10        10x18       105x10 
6.    19  x  10        10  x  21       206  x  10 
c.    23x10        10x32       307x10 

Dividing  by  10 

D 

10x121 
10  x  343 
10x565 

To  divide  by  10  a  number  ending 
reject  the  final  cipher  in  the  dividend 

Thus  170  +  10  =  17;           280  + 

in  a  cipher 
10  =-28. 

i.    Give  quotients  : 
ABC 

a.    180  +  10     600  +  10      180  +  18 
6.   210  +  10     790-*-  10      210  +  21 
c.    350  +  10     800  +  10      340  +  34 

D 
1,800  +  10 
1,950  +  10 
2,160  +  10 

MULTIPLICATION  89 

Multiplying  by  a  Multiple  of  10 

A  dealer  bought  30  boxes  of  pens.     Each  box  con- 
tained 144  pens.     How  many  pens  did  he  buy  ? 


PROCESS 

The  product  by  0  is  0.    Write  0  under  144  pens 

the  0.     Place  the  right-hand   figure  of  X  30 

the  product  by  3  under  the  3.  Ans.  4,320  pens 


Sight  Exercises 


Give  products  : 

A 

B 

c 

D 

a.    26x10 

11x60 

33x30 

50x11 

6.    43x20 

11x70 

22x40 

20x44 

c.   32x30 

11x80 

34x20 

40x12 

d.   21x40 

11x90 

31x30 

30x13 

Sight  Problems 

1.  How  many  hours  in  2  days  ?     In  20  days  ? 

2.  How  many  inches  in  3  feet  ?     In  30  feet  ? 

3.  How  many  ounces  in  10  pounds  ? 

4.  How  many  pens  in  40  dozen  ? 

5.  Find  the  cost  of  50  yards  at  1 1  cents  per  yard. 

6.  How  many  minutes  in  10  hours  ? 

7.  How  many  miles  will  a  train  go  in  20  hours  at 
the  rate  of  43  miles  per  hour  ? 

8.  At  14  bushels  to  the  acre,  how  many  bushels  of 
wheat  will  20  acres  yield  ? 


90  SECTION  TWO 

Written  Exercises 


Find  products  : 


A 

a.   325 
x30 

&.    119 

x80 

B 

234 
x40 

C 

186 
x  50 

'l23 

x  80 

7T7 

D 

157 
x60 

135 
x70 

E 

128 
x70 

108 
x  90 

164 
x  60 

< 

Written  Problems 

1.  Change  (a)  40  days  to  hours;    (6)  80  feet  to 
inches  ;  (c)  60  pounds  to  ounces. 

2.  Find  the  cost  of  50  yards  of  dress  goods  at  28 
cents  per  yard. 


PROCESS 

Write  28  cents,  using  the  dollar  mark  and  $    -^o 

the  decimal  point.    Place  a  decimal  point  in  X  50 

the  product  under  the  one  in  the  multiplicand.  $  \  4.00 


3.  How    much   will    be    paid   for  27   pounds   of 
butter  at  30  cents  a  pound? 

4.  A  dealer  sold  30  yards  of  cloth  at  $2.75  per 
yard.     What  did  he  receive  for  it  ? 

5.  A  man  receives   $3.50   per  day.     How  much 
does  he  earn  in  February  if  he  works  20  days? 

6.  What  is  the  cost  of  40  yards  of  carpet  at  $  1.25 
per  yard  ? 

7.  At  $3.75  a  foot,  what  is  the  cost  of  an  iron 
fence  70  feet  long  ? 


DIVISION  91 

Dividing  by  a  Multiple  of  10 

Sight  Exercises 
Give  quotients : 

A         B         c         D 
a.  10)260     50)550     30)960     20)860 

6.  40)880     20)680     70)70ff     80)88Q 
c.  30)930     40)840     20)880     90)990 

Oral  Exercises 

1.  How  many  times  are  (a)  2  tens   contained  in 
8   tens?     (6)  3  tens  in  12   tens?     (c)  4  tens  in  88 
tens  ?     (d)  6  tens  in  60  tens  ?     (e)  2  tens  in  88  tens  ? 

2.  What  is  the  quotient  (a)  of  8  cents -s- 2  cents? 
(6)  Of  8  dimes -H  4  dimes?     (c)  Of  6  tens -i- 3  tens? 

Written  Exercises 

i.  A  baseball  stand  contained  4200  seats.  They 
were  arranged  in  30  sections.  How  many  seats  were 
in  a  section  ? 


PROCESS 


3IOM20IO  seats       ^ut  °^  ^  a  ver^ca^  line  the  final 
cipher  in  both  the  divisor  and  the  divi- 
Ans.  140    seats   , r  ,     m,  .  .         .„  , 

dend.     The  numbers  remaining  will  be 

3  (the  new  divisor)  and  420  (the  new  dividend). 


ABC 
a.   50)1,350        20)6,940        40)9,760 

6.    60)9,660        20)9,760        90)9,720 
c.    50)8,000        40)9,800        30)9,540 


92 


SECTION   TWO 


Inexact  Division 
i.   Divide  9,810  by  80. 


PROCESS 


When   there   is   a  remainder,  write 

o|U)9ol|U  the  complete  remainder,  including  the 

122^-g-   A.US.  cipher  cut  off,  over  the  original  divisor. 


NOTE.  While  performing  the  division  the  pupil  need  only  con- 
sider the  divisor  as  8  and  the  dividend  as  981,  instead  of  8  tens  and 
981  tens ;  but,  at  this  stage  the  5  tens  remaining  should  be  written  as 
50  over  the  divisor  8  tens,  written  as  80. 


a.  20)9,910 
d.  30)9,910 
2.  Divide  9,9 11  by  70. 


c.   60)9,910 
/.   70)9,910 


PROCESS 

7 [0)991 1 1  Since    the    dividend   does   not   end  in  a 

cipher,  there  must  be  a  remainder.     In  this 

TO"    case  write  the  1  cut  7|0>)991|1 

off  over  the  70.     When  the  division 


is  performed,  write  before  the  1,  the 

4  tens  remaining,  making  the  remainder  41. 


141ft 


Ans. 


«.  40)2,316 

d.  50)3,742 

g.  30)6,418 

j.  20)5,437 


6.  70)5,864 

e.  60)3,915 

k.  50)7,218 

k.  40)6,351 


c.  80)6,873 

/  90)7,777 

i.  70)8,326 

I  60)4,987 


MEASUREMENTS 


93 


Areas  of  Rectangles 
Oral  Exercises 

1.  How      many      postage 
stamps   in   a   sheet    7    stamps 
long,  4  stamps  wide? 

2.  How  many  square  yards 
are  there  in  a  floor  .10  yards 
long,  8  yards  wide  ? 

3.  How  many  square  feet  in  the  surface  of  a  board 
16  feet  long,  -|  foot  wide  ? 

4.  How  many  boards  \  foot  wide  will  cover  a  floor 
12  feet  wide? 

5.  Find  the  area  of  a  fence  20  feet  long,  6  feet 
high. 

6.  How  many  square  feet  of  cloth  will  be  required 
to  cover  the  top  of  a  table  4  feet  long,  2^  feet  wide  ? 

7.  The  top  of  a  paving  brick  is  8  inches  long,  4 
inches  wide.     How  many  square  inches  will  it  cover  ? 

8.  The  side  of  a  paving  brick  is  8  inches  long, 
2J  inches  high.      How  many  square  inches  does  it 
contain  ? 

9.  How  many  square  inches  are  there  in  the  end 
of  a  brick  whose  dimensions  are  4  inches  by  2J  inches  ? 

10.  How  many  square  yards  are  there  in  a  play- 
ground 24  yards  long,  20  yards  wide  ? 

11.  How  many  square  yards  of  matting  will  cover 
a  hall  10  yards  long,  2 \  yards  wide  ? 


94 


SECTION  TWO 
Fractional  Parts 


To  divide  a  thing  into  halves,  it  is  divided  into 
two  equal  parts ;  to  divide  a  thing  into  quarters,  it  is 
divided  into  four  equal  parts;  to  divide  a  thing  into 
thirds,  it  is  divided  into  three  equal  parts. 

i.  Draw  a  rectangle,  4  inches  long  and  3  inches 
wide.  How  many  square  inches  does  it 
contain  ? 

2.  How  many  square  inches  are  there 
in  each  horizontal  row  of  squares  ?  In 
each  vertical  row? 

3.  What  part  of  the  whole  rectangle  is  each  verti- 
cal row  of  squares  ?     What  part  are  two  vertical  rows  ? 
Three  vertical  rows  ? 

4.  What  part  of  the  whole  rectangle  is  one  horizon- 
tal row  of  squares  ?     Two  horizontal  rows  ? 


Three  fourths  is  written 
Two  thirds  is  written    . 


5.  One  third  of  12  squares  is  4  squares ;  how  many 
squares  are  2  thirds  of  12  squares?  One  fourth  of 
12  squares  is  3  squares;  how  many  squares  are  3 
fourths  of  12  squares? 


FRACTIONAL  PARTS  95 

Oral  Exercises 

1.  Give  answers : 

A  B  C  D 

a.  I  of  12  J-  of  15  f  of  15  J  of  16 

b.  |  of  16  J  of  15  f  of  15  f  of  15 

c.  f  of  15  £  of  18  i  of  18  |  of  18 

d.  $  of  16  f  of  16  J-  of  20  |  of  20 

2.  How  many  inches  (a)  in  \  foot  ?     (6)   J  foot  ? 
(c)lfoot?     (d)Jfoot?     (e)  |  foot? 

3.  How  many  ounces  (a)    in   J   pound?     (&)   J- 
pound  ?     (c)  j-  pound  ?     (d)  -f  pound  ?     (e)  %  pound  ? 

4.  How  many  quarts  (a)  in  \  peck  ?     (6)  \  peck  ? 
(c)  J  peck  ? 

5.  What  part  of  a  foot  is  (a)  6  inches?     (6)  4 
inches  ?     (c)  3  inches  ?     (d)  9  inches  ?     (e)  8  inches  ? 

e.   What  part  of  a  pound  is  (a)  8  ounces  ?     (6)  4 
ounces?     (c)  12  ounces? 

7.  What  part  of  a  peck  is  (a)  2  quarts  ?     (b)  4 
quarts?     (c)  6  quarts? 

8.  If  a  bushel  of  oats   weighs  32  pounds,  how 
many  pounds  does  (a)  a  peck  weigh  ?     (b)  A  quart  ? 

9.  If  a  gallon  of  water  weighs  8  pounds,  what  does 
(a)  a  pint  weigh  ?     (b)  A  quart  ? 

10.  How  many  pounds  in  J  bushel  of  potatoes  if  a 
bushel  weighs  60  pounds  ? 

11.  If  2  pecks  of  wheat  weigh  30  pounds,  what 
is  the  weight  of  a  bushel  ? 


96  SECTION  TWO 

Denominate  Numbers 
Oral  Exercises 

1.  How  many  hours   (a)  in  a  day  and  a  half? 
(6)  In  1  day  12  hours? 

2.  How  many  pints  in  a  gallon  ? 

3.  How  many  quarts  (a)  in  3  gallons?     (6)  In  3 
gallons  2  quarts  ? 

4.  How  many  quarts  (a)  in  2  pecks  ?     (6)  In  3 
pecks  ?     (c)  In  4  pecks  ?     (d)  In  a  bushel  ? 

5.  How  many  eggs  (a)  in  3   dozen?      (6)  In  4 
dozen  ? 

6.  How  many  days  (a)  in  7  weeks  1  day  ?     (6)  In 
1 1  weeks  ? 

7.  How   many   weeks    (d)    in   February,    1915  ? 

(b)  How  many  weeks  in  January,  and  how  many  days 
over? 

8.  Change  4  feet  2  inches  to  inches. 

9.  Change  1  pound  6  ounces  to  ounces. 

10.  How  many  inches  (a)  in  2  feet?     (6)  In  3  feet  ? 

(c)  In  a  yard  ? 

11.  How  many  minutes  (a)  in  J  hour  ?     (6)  In  f- 
hour  ? 

12.  What  part  of  a  day  is  (a)  6  hours?     (6)  12 
hours  ?     (c)  18  hours  ? 

is.    Change  160  ounces  to  pounds. 

14.  Change  169  ounces  to  pounds  and  ounces. 

15.  Change  32  feet  to  yards  and  feet. 


DENOMINATE   NUMBERS  97 

Written  Exercises 

1.  How  many  hours  (a)  in  2J  days?     (6)  In  2 
days  12  hours? 

2.  (a)  How    many  quarts   in    13    gallons?     (6) 
How  many  pints  ? 

3.  How  many  quarts  (a)  in  16  gallons?     (6)  In 
16  gallons  2  quarts? 

4.  How  many  quarts  (a)  in  12  pecks?     (b)  In  3 
bushels? 

5.  How  many   eggs    (a)  in  8  dozen?     (b)  In   7 
dozen  and  a  half  ? 

6.  How  many  days  (a)  in  14  weeks  ?     (6)  In  14 
weeks  2  days  ? 

7.  (a)    How  many  weeks  in  a  year  of  365  days, 
and  how  many  days  over  ?     (b)  How  many  days  over 
in  leap  year,  366  days  ? 

8.  Change  8  feet  3  inches  to  inches. 

9.  Change  3  pounds  2  ounces  to  ounces. 

10.  How  many  inches  (a)  in  2  yards?     (b)  In  ^ 
yard?     (c)  In  2J  yards? 

11.  How  many  minutes   (a)  in  ^  hour?     (6)  In 
f  hour?     (c)  In  f  hour?     (d)  In  £  hour? 

12.  What   part   of   an   hour   is    (a)    12   minutes? 
(6)  24  minutes  ?     (c)  36  minutes  ?     (d)  48  minutes  ? 

13.  How  many  bushels  in  64  pecks  ? 

14.  (a)  How  many  gallons  in  64  quarts  ?     (b)  How 
many  pints? 


98 


SECTIOX  TWO 


Rectangular  Solids 
Oral  Exercises 

A  cube  each  of  whose  edges  measures  1  inch  con- 
tains 1  cubic  inch. 


One 

Cubic 

Inch 


i.  How  many  faces  has  a 
cube  ?  How  many  edges  ? 
What  is  the  length  of  each 
edge  of  a  one-inch  cube  ? 
How  long  is  each  face? 
How  wide? 


2.  How  many  one-inch  cubes  will  it  take  to  make 
a  cube  3   inches  long,  3  inches  wide,  and  3  inches 
high?      How   many   one-inch  cubes  in  the  bottom 
layer?     In  the  top  layer? 

3.  How  many  one-inch  cubes  will  it  take  to  cover 
the  bottom  of  a  box  4  inches  long,  3  inches  wide  ? 
If  the  box  is  2  inches  high,  how  many  one-inch  cubes 
will  it  take  to  fill  the  box  ? 

4.  How  many  cubes  of  loaf  sugar  will  fill  a  box 
that  will  hold  6  layers,  each  layer  containing  10  rows 
of  8  cubes  each  ? 

5.  A  pile  of  bricks  is  10  bricks  long.     It  contains 
6  rows  to  a  layer,  and  is  4  layers  high.     How  many 
bricks  are  there  in  the  pile  ? 


SECTION  III 
Reading  and  Writing  Numbers 

Read  the  following : 

Oral  Exercises 


A 

B 

c 

D 

E 

a. 

10,000 

50,590 

10,008 

23,406 

35,600 

6. 

11,000 

61,725 

11,017 

44,444 

52,983 

c. 

20,000 

70,354 

22,034 

53,007 

72,500 

d. 

31,000 

83,976 

36,090 

85,021 

93,811 

e. 

54,000 

92,417 

40,003 

11,642 

64,300 

Written  Exercises 
Write  in  figures : 

1.  Sixty-one  thousand. 

2.  Fifty-three  thousand  seven  hundred. 

3.  Forty  thousand  sixty. 

4.  Thirty-two  thousand  nine. 

5.  Twelve  thousand  three  hundred  forty-five. 

6.  Seventy  thousand  seven. 

7.  Eighty-eight  thousand   eight    hundred   eighty- 
eight. 

8.  Ninety-one    thousand    seven   hundred   twenty- 
seven. 

90 


100  SECTION  THREE 

Multipliers  of  Two  Figures 

i.   Each  of  467  pieces  of  copper  wire  weighs  21 
ounces.     What  is  their  total  weight  ? 


PROCESS 

Multiply  by  1,   placing  the  right-hand  467  OZ. 

figure  of  the  product  under  the  1.    Multiply  x  2 1 

by  2  tens,  placing  the  right-hand  figure  of 
the  product  under  the  2.  Combine  the  par- 
tial products. 

Am.  9,807  oz. 


Written  Exercises 

2.    Find  products : 

Test  by  performing  the  multiplication  a  second 
time  without  referring  to  the  first  operation  until  the 
product  is  again  obtained. 


v*  . 

A 

B 

C 

D 

a. 

444  x 

22 

184 

x 

53 

132 

x 

75 

121 

x82 

6. 

468  x 

21 

186 

x 

52 

134 

X 

74 

122 

x81 

c. 

222  x 

33 

195 

X 

51 

136 

X 

73 

101 

x99 

d. 

308  x 

32 

143 

X 

66 

138 

X 

72 

102 

x98 

e. 

316x 

31 

151 

X 

65 

139 

X 

71 

103 

x97 

f. 

225  x 

44 

156 

X 

64 

111 

X 

88 

104 

x96 

g- 

231  x 

43 

158 

X 

63 

112 

X 

87 

105 

x95 

h. 

222  x 

42 

161 

X 

62 

113 

X 

86 

106 

x94 

i. 

237  x 

41 

163 

X 

61 

116 

X 

85 

107 

x93 

j- 

123  x 

55 

128 

X 

77 

118 

X 

84 

108 

x92 

k. 

172  x 

54 

131 

X 

76 

119 

X 

83 

109 

x91 

REVIEWS 
Sight  Drills 

101 

1 

.    Multiply  : 

^ 

B 

c 

D 

E           F 

G 

H 

a. 

90 

80 

70 

60 

50        40 

30 

20 

x2 

x3 

x4 

x5 

x6       x7 

x8 

x9 

f 
&. 

84 

93 

72 

61 

41        51 

31 

21 

x2 

x3 

x4 

x5 

x6       x7 

x8 

x9 

c. 

94 

83 

62 

71 

31        21 

41 

51 

x2 

x3 

x4 

x5 

x6      x7 

x8 

x9 

2. 

,    Divide  : 

£ 

180 

240 

360 

350 

360 

280 

320 

20 

30 

40 

50 

60 

70 

80 

e. 

126 

279 

246 

357 

305 

497 

324 

21 

31 

41 

51 

61 

71 

81 

/• 

630 

819 

243 

568 

183 

255 

164 

90 

91 

81 

71 

61 

51 

41 

3. 

Give 

quotients  and  remainders  : 

0- 

190 

248 

186 

248 

369 

357 

460 

21 

41 

61 

81 

91 

71 

51 

A. 

250 

250 

460 

330 

360 

150 

290 

31 

61 

91 

81 

51 

21 

71 

i 

100 

200 

300 

400 

400 

400 

400 

99 

99 

99 

99 

98 

97 

96 

102  SECTION  THREE 

Sight  Problems 

1.  At  32  to  a  class,  how  many  pupils  are  there 
in  4  classes  ? 

2.  At  the  rate  of  21  miles  per  hour,  how  long 
would  a  trolley  car  require  to  go  147  miles  ? 

3.  Find  the  cost  of  6  acres  of  land  at   $61   per 
acre. 

4.  How  many  suits  of  clothes  at  $21  each  can 
be  bought  for  $168? 

5.  What  is  the  total  weight  of  6  tubs  of  butter  if 
each  weighs  51  pounds? 

6.  How  many  barrels  will  hold  369  gallons  of  oil 
if  each  holds  41  gallons  ? 

7.  How  many  yards  around  the  4  sides  of  a  square 
each  side  of  which  measures  92  yards  ? 

8.  If  a  conductor  receives  $  4.05  from  81  passen- 
gers, what  does  each  pay  ? 

9.  At  51  nails  to  the  pound,  how  many  pounds  will 
459  nails  weigh  ? 

10.  How  many  nails  in  8  pounds  if  there  are  61 
nails  to  the  pound  ? 

11.  A  piece  of  rope  126  yards  long  is  divided  into 
42  pieces.     How  many  yards  in  each  piece  ? 

12.  How   many   quarts  of  milk  are  there  in  72 
gallon-cans  ? 

13.  At  32  pounds  to  the  bushel,  how  many  bushels 
of  oats  will  weigh  128  pounds  ? 


REVIEWS  103 

14.    How  many  21 -acre  fields  are  there  in  a  farm 
of  189  acres  ? 

is.    How  far  does  a  train  travel  in.  4  hours  at  the 
rate  of  42  miles  per  hour  ? 

16.  At  41  bushels  to  the  acre,  how  many  acres  will 
produce  328  bushels  of  corn  ? 

17.  If  a  family  uses  3  quarts  of  milk  a  day,  how 
many  quarts  are  used  in  July  ? 

is.    How  many  hours  would  a  train  require  to  go 
128  miles  at  the  rate  of  32  miles  per  hour? 

19.  If  5  men  require  41   hours  to  do  a  piece  of 
work,  how  long  would  it  take  1  man  to  do  it  ? 

20.  What  part  of  276  is  92  ? 

21.  Find  the  cost  of  72  2-cent  postage  stamps. 

22.  At  99  cents  each,  how  many  baseballs  can  be 
bought  for  $  10,  and  how  much  change  will  there  be  ? 

23.  If  a  hogshead  contains  63  gallons,  how  many 
hogsheads  are  there  in  189  gallons? 

24.  If    1    fourth   of   a  number  is  40,  what  is  3 
fourths  of  the  number? 


120 


25.  If  3  fourths  of  a  number  is  120,  what  is  1 
fourth  of  the  number  ?     What  is  the  number  ? 

26.  What  part  of  120  is  40  ?    What  part  of  120 
is  30  ?     What  part  of  120  is  90  ? 


104  SECTION  THREE 

Long  Division 

i.  A  pile  of  copper  wire  pieces  weighs  9,807  ounces. 
If  each  piece  weighs  21  ounces,  how  many  pieces  in 
the  pile  ? 


PROCESS 

Ans".   467  (pieces)     Take  98  as  tlie  first  partial  dividend  and 
21^9807          divide  it  by  21.     Write  4,  the  first  quotient 
ft  .  figure,  above  the  8.     Multiply  21  by  4,  and 

place  the  product  84  under  98.     Subtract  84 
from  98,  and  to  the  remainder  14  annex  0,  the 
126  next  figure  of  the  dividend,  which  makes  140, 

147  the  second  partial  dividend.  Divide  140  by 
21,  and  write  the  quotient  6  above  the  0. 
Multiply  21  by  6  and  place  the  product  126 
under  140.  Subtract  126  from  140,  and  to  the 
remainder  14  annex  7,  the  remaining  figure  of  the  dividend, 
which  makes  147  the  next  partial  dividend.  Divide  147  by 
21  and  write  the  quotient  7  above  the  7.  Multiply  21  by  7 
and  place  the  product  147  under  147.  As  this  is  the  same 
as  the  last  partial  dividend,  there  is  no  remainder.  The 
quotient  is,  therefore,  467.  Write  pieces  in  parenthesis. 


Ans.  286  Ans.  153  Ans.  137    Ans.  123 

34)9724  53)8109  72)9864     81)9963 

68  53  72        81 

292  280  266 

272  265  216 


204        159        504 
204        159        504 

Write  each  figure  in  the  quotient  directly  over  the  last  figure  of  the 
partial  dividend  that  produces  it. 


LONG  DIVISION  105 

Testing  Quotients 


Test 

Quotient      286 
Divisor      x  34 

153 
x53 

137 

x72 

123 

x81 

1144 

459 

274 

123 

858 

765 

959 

984 

Dividend   9724 

8109 

9864 

9963 

2.    Find  quotients  : 

A 

B 

c 

D 

a. 

462-21 

714-5-51 

1,701-81 

3,936  -  32 

b. 

483-21 

867-5-51 

2,592-81 

8,946- 

-42 

c. 

672-21 

612-5-51 

3,483-81 

9,828  - 

-42 

d. 

693-^-21 

918-5-51 

4,374-81 

6,604  - 

-52 

e. 

882-*-  21 

816-5-51 

5,278-91 

1,820- 

-52 

/ 

651-5-31 

6,832-5-61 

1,092-91 

6,552  - 

-52 

9- 

961-31 

1,403-5-61 

2,002-91 

1,352- 

-52 

h. 

682-5-31 

8,174-61 

1,183-91 

2,232  - 

-62 

i. 

992-*-  31 

2,745-5-61 

3,003-91 

1,550- 

-62 

j- 

713-31 

9,516-5-61 

4,004-91 

2,914-62 

k. 

943-5-41 

7,881-71 

7,612-22 

1,944-72 

I 

533-5-41 

1,562-71 

3,476-5-22 

5,184-72 

m. 

984-5-41 

9,514-5-71 

5,588-22 

1,476-5-82 

n. 

902-5-41 

1,775-5-71 

4,352-32 

6,806-5-82 

0. 

861-5-41 

9,656-*-  71 

7,488-5-32 

6,900-5-92 

P- 

561-*-51 

l,704-»-71 

7,104-5-32 

2,208-5-92 

3- 

612^51 

9,372-5-71 

4,224-5-32 

4,416-5-92 

o 


106  SECTION  THREE 

More  than  One  Operation 
Sight  Problems 

1.  John  has  12  marbles;  James  has  5  more  than 
John.     How  many  marbles  have  both  ? 

2.  If  a  girl  saves  3  cents  per  day,  how  much  less 
than  a  dollar  does  she  save  in  October  ? 

3.  If  a  boy  saves   2    cents  per  day,  how  much 
more  than  a  half  dollar  does  he  save  in  October  ? 

4.  How  many  days  in  the  first  three  months  of 
1916?     (Leap  year.) 

s.    How  many  days  in  April,  May,  and  June  ? 

6.  From  a  40-quart  can  of  milk  there  have  been 
sold  8  gallons.     How  many  quarts  remain  ? 

7.  What  number  divided  by  21  gives  a  quotient 
of  4  and  a  remainder  of  6  ? 

8.  A  man  has  39  cows  in  three  fields.     In  one 
field  he  has  12  cows;  in  another  field  he  has  14  cows. 
How  many  cows  in  the  third  field  ? 

9.  If  a  traveler's  expenses  are  $3  per  day,  how 
much  does  he  spend  in  three  weeks  ? 

10.  Mary  has  as  much  more  than  25  cents  as  Jane 
has  less  than  25  cents.     If  Mary  has  32  cents,  how 
much  has  Jane  ? 

11.  What  must  be  added  to  21  to  obtain  the  dif- 
ference between  15  and  58  ? 

12.  If  8  pounds  of  sugar  cost  48  cents,  how  many 
pounds  can  be  bought  for  60  cents  ? 


REVIEWS  107 

Written  Problems 

1.  William  has  25  marbles;  Thomas  has  16  more 
than  William.     How  many  marbles  have  both  ? 

2.  If  a  girl  saves  3  cents  a  day,  how  much  more 
than  50  cents  does  she  save  in  February,  1916  ? 

3.  If  a  boy  saves  4  cents  a  day  in  February,  1915? 
how  much  less  than  $  2  does  he  save  ? 

4.  How  many  days  in  the  first  six  months  of  1914  ? 

5.  How  many  days  in  the  last  six  months  of  1915  ? 

6.  From  a  41 -gallon  barrel  of  oil  there  have  been 
sold  48  quarts.     How  many  gallons  remain  ? 

7.  What  number  divided  by  21  gives  a  quotient 
of  3  and  a  remainder  of  17  ? 

8.  A  man  has  60  cows  in  three  fields.     In  one 
field  he  has  17  cows,  in  another  he  has  27  cows.    How 
many  has  he  in  the  third  field  ? 

9.  If  a  traveler's  expenses  are  $  4  per  day,  how 
much  does  he  spend  in  7  weeks  ? 

10.  Sarah  has  as  much  more  than  75  cents  as  Laura 
has  less  than  75  cents.     If  Laura  has  58  cents,  how 
much  has  Sarah  ? 

11.  What  must  be  added  to  39  to  obtain  the  differ- 
ence between  17  and  91  ? 

12.  If  3  pounds  of  coffee  cost  72  cents,  how  many 
pounds  can  be  bought  for  96  cents  ? 

13.  When  a  16  pound  bag  of  sugar  is  worth  96 
cents,  what  is  the  cost  of  13  pounds? 


108  SECTION  THREE 

Long  Division 

i.  A  machine  turns  out  8,649  feet  of  wire  in  83 
minutes.  What  is  the  output  per  minute  ?  What  is 
the  production  per  minute  when  9,499  feet  are  de- 
livered in  73  minutes  ? 


PROCESS 


Am.   104£J  ft.      Place  the  first  quotient  Ans.  130T9¥  ft. 
83)8649  ft.      figure  over  the  right-hand    73)9499  ft. 
00                 figure  of  the  first  partial           nrt 
oo                       ,              j               ,.                 (6 
• product,  and   a  quotient  

040  O1 Q 

figure  over  each   of  the 
remaining  figures  of  the 
17  dividend,  writing  a  cipher  9 

when  a  partial  dividend 
does  not  contain  the 
divisor. 

TEST 

104  Quotient  Test   the   result     130  Quotient 

x  83  Divisor       bv  addins  the  re'  x  73  Divisor 
Q  mainder  to  the  prod- .  Qa 

•  >  I  _  p  ,1  ,  •  OiJU 

uct  of  the  quotient 

832  by  the  divisor.    The  910 

8632  sum  will  equal  the  9490 

+  17  Remainder  dividend  if  the  work     +9  Remainder 
Dividend     is  correct  9 499  Dividend 


2.    Divide : 

a.  7,656  +  25    c.  7,000  +  66    e.  2,000-*- 19 

6.  7,358  +  35    d.  9,400  +  77    /.  7,009  +  28 


REVIEWS 


109 


Addition  and  Subtraction 
Sight  Drills 

For  daily  drills  a  chart  similar  to  the  following  may  be  prepared : 
ABODE  F  G  H 


a. 
b. 

G. 
d. 

e. 
/ 

9- 

h. 


2 

13 

25 

39 

48 

57 

64 

76 

3 
5 

15 

29 

38 

47 

54 

66 

72 

19 

28 

37 

44 

56 

62 

73 

9 

18 

27 

34 

46 

52 

63 

75 

8 

17 

24 

36 

42 

53 

65 

79 

7 
4 

14 

26 

32 

43 

55 

69 

78 

16 

22 

33 

45 

59 

68 

77 

6 

12 

23 

35 

49 

58 

67 

74 

1.  Add  to  each  of  the  numbers  in  the  table : 

ABCDEFGH 

50    41    32    23    14    25    36    47 
60    51    42    33    24    35    46    57 

To  the  order,  "  Add  50  by  lines,"  successive  pupils  answer  rapidly : 
52,  63,  75,  etc. ;  53,  65,  79,  etc.  To  the  order,  "  Add  47  by  columns," 
the  replies  are :  49,  50,  52,  etc. ;  60,  62,  66,  etc. 

2.  Subtract  each  of  the  numbers  in  the  table  from 

99        91         95        89         96        87        98        85 
92         97         90         94         88         93         86         84 

The  order  here  is :  "  Take  from  99  by  lines  "  or  "  Take  from  91  by 
columns." 


110 


SECTION   THREE 


Oral  Exercises 

NOTE.     Combine  with  the  entire  first  number  the  tens  of  the 
second  number,  then  the  ones. 

Thus  86  +  53  =  86  +  50(136)  +  3  =  139. 
Also  86  -  53  =  86  -  50(36)  -  3  =  33. 


i.  Add: 

A 

B 

c 

D 

E 

a. 

30  +  80 

70  +  65 

42  +  93 

73  +  66 

54  +  72 

6. 

40  +  90 

85  +  90 

71  +  65 

81+98 

65  +  33 

c. 

70  +  60 

60  +  54 

82  +  93 

63  +  54 

76  +  82 

d. 

80  +  90 

37  +  80 

63  +  53 

35  +  82 

82  +  21 

2.    Subtract : 

e.    90-30      85-35  49-23  99-19 

/.    80-40      74-40  68-34  86-21 

g.   70-20      63-23  87-45  70-23 

h.   60-30      72-30  56-22  66-23 


3.   Add: 

A 

i.   40^  +  70^ 


k.   60^  +  60^ 


B  C 

50^  +  85^  31^  +  63^ 

65^  +  60^  42^  +  52^ 

70^  +  35^  53^  +  46^ 

85^  +  40^  64^  +  33^ 


4.    Subtract : 
A 

m.  $1.10-$  .30 

n.  $1.80 -$1.50 

o.  $1.20-$  .70 

p.  $1.80 -$1.60 


34-13 
55-22 
94-33 
86-25 


$1.05 -$.50 
$1.06- $.86 
$1.07- $.70 

$1.08 -$.48 


C 

94^-32^ 
87^-63^ 


69^-46^ 


REVIEWS  111 

Oral  Problems 

1.  There  are   35  boys  and   30  girls  in  a  school. 
How  many  pupils  are  there  ? 

2.  In  a  school  of  86  pupils,  42  are  girls.     How 
many  are  boys  ? 

3.  When  a  boy  saves  30  cents  more,  he  will  have 
a  dollar.     How  much  has  he  now  ? 

4.  A  girl  has  read  35  pages  in  her  reader  and  she 
has  60  more  to  read.     How  many  pages  are  there  in 
the  book  ? 

5.  If  I  pay  5  hundred  dollars  for  one  lot  and  4 
hundred  dollars  for  another,  what  do  I  pay  for  both  ? 

6.  Of  a  farm  of  96  acres,  40  acres  are  in  wheat 
and  the  rest  in  corn.     How  many  acres  are  there  in 
corn? 

7.  A  conductor  collected  47  fares  going  out,  and 
coming  back,  40  fares.     How  many  did  he  collect  on 
the  round  trip? 

8.  There  are  42  telephone  poles  on  one  side  of 
the  road  and  36  telegraph  poles  on  the  other  side. 
How  many  poles  are  there  on  both  sides  ? 

9.  A  farmer  has  42  cows.     How  many  must  he 
buy  in  order  to  have  65  ? 

10.  How  many  are  23  and  23  ? 

11.  A  grocer  mixed  40  pounds  of  black  tea  with 
25  pounds  of  green  tea.     How  many  pounds  of  mixed 
tea  were  there  ? 


112  SECTION  THREE 

Dollars  and  Cents 
Written  Exercises 


i.   Add. 

Test  results  : 

^ 

B 

c 

D 

E 

a. 

$36.85 

$    7.44 

$  25.82 

$31.25 

$   8.47 

6.95 

8.82 

5.33 

9.45 

20.00 

18.26 

18.25 

20.31 

10.24 

5.78 

5.37 

4.76 

2.59 

7.13 

.29 

7.44 

37.53 

.45 

8.88 

48.86 

&. 

$11.47 

$35.79 

$18.27 

$5.10 

$  48.74 

10.83 

3.46 

3.42 

43.83 

.09 

45.09 

11.89 

20.35 

7.65 

6.85 

7.67 

6.34 

2.87 

17.25 

.77 

8.54 

9.95 

28.92 

5.74 

13.24 

.98 

8.87 

4.73 

18.29 

7.65 

c. 

$29.99 

$  12.25 

$25.26 

$10.79 

$   3.89 

14.89 

8.24 

8.43 

3.04 

22.50 

2.46 

5.83 

.24 

13.40 

6.18 

.25 

16.79 

53.10 

7.44 

20.06 

25.57 

9.86 

1.75 

8.26 

.88 

3.21 

43.50 

.89 

.29 

9.47 

d. 

$36.46 

$9.32 

$  13.08 

$  12.46 

$17.27 

5.16 

8.56 

3.15 

13.81 

6.66 

8.17 

42.97 

11.48 

11.36 

.75 

9.10 

2.73 

5.27 

1.88 

24.00 

29.13 

9.37 

5.21 

.75 

4.44 

6.48 

10.66 

40.69 

29.95 

.98 

FEDERAL  MONEY  113 

2.    Subtract.     Test : 


A 

B 

c 

D 

E 

a. 

$90 

.00       $ 

87.50 

$75, 

.98       $56.03 

$47 

.96 

-8 

.47       - 

29 

.43 

-47. 

99 

27. 

06 

-8 

.89 

6. 

$81 

.62       $53 

.70 

$45, 

,76       $ 

47.57 

$30 

.13 

-51 

.77        -9 

.84 

-17 

.89 

30. 

75 

-25 

.08 

c. 

$  36.80       $ 

52.23 

$93, 

,2o       «f> 

85. 

64 

$92 

.73 

-19 

.95      - 

27 

.26 

-47 

.65      - 

43.76 

-50 

.95 

3.    Multiply. 

Test: 

Point  off  two 

places 

in  the 

answer 

for 

cents 

• 

A 

B 

c 

D 

E 

a. 

$14 

.09       $ 

12 

.48 

$11. 

,59        1 

;io 

.83 

$9 

.84 

x7 

x8 

x7 

x9 

X 

10 

I. 

$7 

.65 

$6 

.45 

$  8. 

90 

$4.32 

$3 

.25 

X 

10 

X 

11 

X 

21 

x31 

X 

41 

4.    Divide.     Test  : 

Place  the  decimal  point  in  the  quotient  when  it  is 
reached  in  the  dividend. 

A  B  CD 

a.     4)  $98.76      5)  $95.75        6)  $96.84        7)$  90.09 


75.12      9)$  96.75      11)$  80.08      12)$  15.12 
c.   21)$  60.06    21)190.09      21)$  48.93      21)$  68.88 


114  SECTION  THREE 

Cents  as  Divisors 
Written  Exercises 

i.   At  5  cents  per  yard,  how  many  yards  can  be 
bought  for  $1.95? 


PROCESS 

cents    cents 


Write  the  divisor  and  the  dividend  as  cents. 
195  cents  contains  5  cents  39  times.  5)195 

Write  yd.  in  a  parenthesis.  A.ns.  39  (yd.) 


2.  At  13  cents  per  pound,  how  many  pounds  of 
pork  can  be  bought  for  $  1.69  ? 

(169  cents  divided  by  13  cents  gives  the  number  of 
pounds.) 

3.  Divide  the  following : 

a.    $3.64n-$.07  e.    $10.50-5-25* 

6.    $  4.84  -*-$.  11  /.    $10.50-*- 42*' 

c.  $4.84-5-$.44  g.    $40.50  +  50* 

d.  $4.41-*- $.21  h.    $17.22-*- 14* 

4.  At  25  cents  each,  how  many  penknives  can  be 
bought  for  $12.75? 

5.  At  13  cents   per  quart,  how   many   quarts  of 
berries  will  $  4.03  pay  for  ? 

6.  At  30  cents  per  quart,  how  many  quarts  of  ice 
cream  can  be  bought  for  $  10.80  ? 

7.  At   5    cents   for   each   fare,   how   many   fares 
amount  to  $3.45? 

8.  At   25   cents  each,   how   many   dolls    can   be 
bought  for  $  6.25  ? 


MEASUREMENTS  115 


Rectangles 

A  rectangle  is  a  figure  of 
four  sides  having  square 
corners. 

The  floor  of  the  classroom 


is  a  rectangle ;  so  is  the  ceiling,  each  wall,  the  door, 
the  window. 

The  opposite  sides  of  a  rectangle  are 
equal  in  length.  When  a  rectangle  has 
four  equal  sides,  it  is  called  a  square. 


To  find  the  area  of  a  rectangle  means  to  find 
the  number  of  square  inches,  square  feet,  square 
yards,  etc.,  it  contains. 


Preparatory  Exercises 

1.  A  square  having  each  side  1  foot  long  contains 
a  square  foot.     How  many  1-foot  squares  can  be  cut 
from  a  piece  of  paper  3  feet  long,  2  feet  wide  ? 

2.  A  square  having  each  side  1  yard  long  contains 
a  square  yard.     How  many  1-yard  squares  can  be  cut 
from  a  piece  of  sheeting  3  yards  long,  2  yards  wide  ? 


To  find  the  number  of  square  inches,  square  feet, 
square  yards,  etc.,  in  the  area  of  a  rectangle  mul- 
tiply the  number  of  inches,  feet,  yards,  etc.,  in  its 
length  by  the  number  of  the  same  denomination  in 
its  width. 


116  SECTION   THREE 

Sight  Exercises 

i.    Give    the    area    of    each    of     the    following 
rectangles : 

a.  10  in.  by  11  in.  /.  10  yd.  by  8  yd. 

&.  14  ft.  by  10  ft.  g.  20  in.  by  12  in. 

c.  20  yd.  by  13  yd.  h.  21  ft.  by  10  ft. 

d.  16  in.  by  10  in.  i.  12  yd.  by  10  yd. 

e.  9  ft.  by  8  ft.  j.  11  in.  by  9  in. 


The  perimeter  of  a  figure  is  the  distance  around  it. 


2.  The  number  of  yards  in  the  perimeter  of  a  field 
20  yards  wide,  24  yards  long  is  20  yd.  +  24  yd.  +  20 
yd. +  24  yd.,  or  88  yd. 

3.  Give   the   perimeter  of   each  of   the  following 
rectangles : 

a.  12  in.  by  10  in.  /.  13  yd.  by  30  yd. 

&.  21  ft.  by  21  ft.  g.  20  in.  by  12  in. 

c.  20  yd.  by  14  yd.  h.  22  ft.  by  22  ft. 

d.  12  in.  by  21  in.  i.  21  yd.  by  13  yd. 

e.  20  ft.  by  30  ft.  >  30  in.  by  40  in. 

4.  What  is  the  length  of  a  room  12  feet  wide  that 
contains  240  square  feet  ? 

5.  Give  the  perimeter  of  a  square  whose  area  is 
100  square  inches. 

6.  How  many  square  yards  of  carpet  are  needed 
to  cover  a  floor  4  yards  wide,  5  yards  long  ? 


MEASUREMENTS  117 


Oral  Problems 

i.    Find   the  perimeter  of  a  so  yd- 

field  30  yards  long,  20  yards 
wide. 


2.  A  rug  contains  140  square 

feet.     If  its  length  is   14  feet,  so  yd. 

what  is  its  width  ? 

3.  A  field  30  yards  long,  20  yards  wide  is  inclosed 
by   a   wire   fence.      How   many  yards  of  wire  are 
needed  for  each  wire  in  the  fence  ? 

4.  How  many  square  inches  of  gilt  paper  are  re- 
quired to  cover  each  of  the  six  square  faces  of  a  cube 
8  inches  long  ? 

5.  A  room  is  20  feet  long,  15  feet  wide,  10  feet 
high. 

a.  How  many  square  feet  are  there  in  each  of  the 
two  side  walls  ? 

b.  How  many  square  feet  are  there  in  each  of  the 
two  end  walls  ? 

c.  How    many    square    feet    are    there    in    the 
ceiling  ? 

d.  How    many    square    feet    of    plastering    are 
required  ? 

e.  How  many  square  feet  of  carpet  are  needed  to 
cover  the  floor  ? 

6.  How  many  square  feet   are   there   in  a   fence 
6  feet  high,  30  feet  long  ? 


118  SECTION   THREE 

Oral  Problems 

1.  Find  the  cost  of  4  pounds  of  tea  at  40  cents  a 
pound. 

2.  I  paid  $  1.20  for  6  pineapples.     What  was  the 
price  of  each  ? 

3.  Andrew  has  90  cents;  Bernard  has  60  cents 
more  than  Andrew.     How  much  has  Bernard  ? 

4.  A   $2    bill   is   given   in   payment   for   goods 
amounting  to  $  1.20.     How  much  change  is  received  ? 

5.  What  is  the  cost  of  J  yard  of  silk  at  the  rate 
of  $1.60  a  yard? 

6.  If  a  man  receives  $2.40  a  day  of  8  hours,  how 
much  is  he  paid  an  hour  ? 

7.  When  goods  cost  $1.60  a  yard,  what  part  of 
a  yard  can  be  bought  for  40  cents  ? 

a.    After  spending  80  cents  I  have  80  cents  left, 
how  much  had  I  at  first  ? 

9.    Find  the  total  cost  of  25  cents'  worth  of  cake 
and  3  pounds  of  candy  at  20  cents  per  pound. 

10.  A  girl  pays  30  cents  for  3  half-pound  boxes  of 
candy.     What  does  the  candy  cost  a  pound  ? 

11.  If   2  feet  of   wire  rope  cost  20  cents,  what 
would  be  the  cost  of  a  yard  ? 

12.  Find  the  cost  of  a  yard  of  ribbon  at  the  rate  of 
20  cents  for  two  thirds  of  a  yard. 

13.  A  farmer  has  80  sheep.     How   many  has  he 
after  he  sells  three  quarters  of  them  ? 


REVIEWS  119 

Written  Problems 

1.  Find  the  cost  of  6  pounds  of  tea  at  45  cents 
per  pound. 

2.  I  paid  $  1.05  for  7  quarts  of  berries.    What  was 
the  price  of  a  quart  ? 

3.  Harry  has  84  cents ;  Fred  has  26  cents  more 
than  Harry.     How  much  money  has  Fred  ? 

4.  I  buy  goods  amounting  to  $  3.85  and  I  give 
the  grocer  a  $5  bill.     How  much  change  do  I  get? 

5.  What  is  the  cost  of  ^  yard  of  velvet  at  $3.50 
per  yard? 

6.  If  a  man  receives  $  2.80  per  day  of  8  hours, 
how  much  is  he  paid  by  the  hour? 

7.  When  goods  cost  $  2.80  per  yard,  what  part  of 
a  yard  can  be  bought  for  35  cents? 

8.  After  giving  his  sister  55  cents,  a  boy  still  has 
$  1.35.     How  much  money  had  he  at  first  ? 

9.  What  is  the   cost  of   3   pounds   of   candy  at 
35  cents  per  pound  and  45  cents'  worth  of  ice  cream? 

10.  A  boy  pays  $1.05  for  3  half-pound  packages 
of  tea.     What  does  the  tea  cost  a  pound? 

11.  If  2  feet  of  wire  cable  cost  38  cents,  what  is 
the  cost  of  a  yard? 

12.  Find  the  cost  of  a  yard  of  silk  at  the  rate  of 
72  cents  for  two  thirds  of  a  yard. 

13.  A  farmer  has  144  sheep.     How  many  would 
he  have  if  he  sold  three  fourths  of  them? 


120 


SECTION  THREE 


Fractional  Parts 
Oral  Exercises 

i.   Draw  a  rectangle  5  inches  long  and  3  inches 
wide,  and  divide  it  into  1-inch  squares. 

2.  (a)  How  many 
squares  are  there  in 
each  horizontal  row  ? 
(&)  How  many  hori- 
zontal rows  are  there? 


(c)  How  many  square 
inches  in  the  rectangle? 

3.  (a)  How  many  squares  are  there  in  each  verti- 
cal column?     (6)  How  many  vertical  columns   are 
there?     (c)  How  many  square  inches  are  5  times  3 
square  inches?     (d)  How  many  square  inches  are  3 
times  5  square  inches? 

4.  (a)  What  part  of  the  rectangle  is  one  horizontal 
row?     (b)  Two  horizontal  rows? 

5.  (a)  What  part  of  the  rectangle  is  one  vertical 
column  ?     (&)  Two  vertical  columns  ?     (c)  Three  ver- 
tical columns  ?     (d)  Four  vertical  columns  ? 

6.  (a)  3  is  what  part  of  15?     (6)  5  is  what  part? 
(c)  6  is  what  part  ?     (d)  9  is  what  part  ?     (e)  10  is 
what  part?     (/)  12  is  what  part? 

7.  a.  £  of  36,  60,  66,  90.       e.  }  of  15,  25,  35,  45. 
6.  |  of  24,  36,  80,  48.       /  f  of    5,  15,  25,  35. 

c.  f  of  12,  18,  24,  30.       g.  f  of  20,  30,  40,  50. 

d.  I  of  16,  20,  32,  40.       h.  J  of  15,  20,  35,  40. 


FRACTIONAL  PARTS  121 

Written  Exercises 


A 

B 

c 

D 

E 

F 

1. 

Find 

i 

of 

276, 

480, 

178, 

360, 

696, 

720. 

2. 

Find 

1 

of 

360, 

297, 

165, 

576, 

480, 

720. 

3. 

Find 

4 

of 

484, 

360, 

576, 

720, 

244, 

676. 

4. 

Find 

i 

of 

510, 

650, 

360, 

720, 

480, 

975. 

5. 

Find 

* 

of 

270, 

444, 

720, 

516, 

888, 

978. 

Find  £  of 

408. 

METHOD 

2 
P 

by 

136 

of  4P£  =  272 

dividing  408 

,  Ans. 

by  3, 

Find  1  third  of  408,  which  is  136, 
and  cancel  these  two   numbers. 

Multiply  136 

by 

2. 

6. 

Find 

1 

of 

342, 

444, 

396, 

165, 

576, 

720. 

7. 

Find 

£ 

of 

480, 

360, 

576, 

720, 

244, 

676. 

8. 

Find 

if 

of 

510, 

650, 

360, 

720, 

480, 

975. 

9. 

Find 

fl 

7T 

of 

510, 

650, 

360, 

720, 

480, 

975. 

10. 

Find 

£ 

of 

510, 

650, 

360, 

720, 

480, 

975. 

11. 

Find 

B 

(> 

of 

360, 

480, 

720, 

516, 

888, 

978. 

12. 

(a)   Find 

*  of 

216. 

0) 

Find 

i  of 

216. 

(c)  Compare  the  two  results. 

13.  (a)  Find   £   of    216.       (b)  Find    £    of    216. 
(c)  Compare  the  results,     (d)  Find  -J  of  216. 

14.  (a)  Find   f    of    216.       (6)  Find    £    of    216. 
(c)  Compare  the  results. 

is.   Find  the  sum  of  J-  of  216  and  J  of  216. 


122  SECTION  THREE 

Mixed  Numbers  Containing  Halves  . 
Preliminary  Exercises 

— •—*__ 

i.    I    buy    one    half 


dollar's    worth   of   tea 
_,_  ,  and   one   half    dollar's 

2  2 

worth  of  sugar.     What 


,    T         <•     i    ,1  o 
do  1  pay  lor  both : 


2.    How   many   half   dollars  (a)  in    $  1  ?      (6)  In 
$2?     (c)  In  $11?     (d)  In  $21? 


,  2J,  etc.,  are  called  mixed  numbers. 


3.  Change  to  a  whole  number  or  to  a  mixed  num- 
ber:  (a)  |.     (6)  f.     (c)  f.     (d)  f. 

4.  A  man  sold  a  pie  and  a  half  to  a  boy,  and  a 
half  pie  to  a  girl.     How  many  did  he  sell  to  both  ? 

5.  A  girl  baked  3  pies.     How  many  of  them  are 
left  after  \  pie  is  eaten  ? 

6.  A  man  earned  $  3  per  day.     He  spent  $  2^  per 
day.     How  much  did  he  save  each  day  ? 

7.  Give  sums  at  sight  : 

a.       3£     6.       31     c.       3£     d.       3£     e.       3J 
+  31  +2  +11  +3  + 


8.    Give  remainders  at  sight  : 
a.       6|     6.       6       c.       61     d.       6       e.       6 
-31  -i  -4  -11  -4J 


ADDITION  OF  MIXED  NUMBERS  123 


Written  Exercises 
f  cloth  contain 
yards.     How  many  yards  in  all  ? 


i.    Three  lots  of  cloth  contained  13J,  6J,  and  29J 


PROCESS 

First  add  the  fractions.     Their  sura  is 
f  ,  which  is  equal  to  1^.     Write  the  frac- 
tion £,  and  carry  1  to  the  column  of  ones, 
pt"/> 

131  yd. 
291 

-4ns. 

491  yd. 

2.   Add  the 

following  : 

*v~4- 

A 

B 

c 

D 

E 

a.   201 

201 

371 

25 

25J 

37 

371 

61 

301 

301 

&.   481 

181 

37J 

231 

17 

371 

m 

561 

151 

181 

c.   631 

551 

27 

1 

23 

8J 

20 

6i 

171 
A<$ 

94 

9J 

17^ 

48 

8J 

64 

d.   20 

37J 

3| 

25J 

17 

364 

20J 

18 

26^ 

6J 

64 

30 

50 

/I  1L 

*  »> 

27 

18 

e.   214 

15i 

1  si- 

30J 

20J 

214 

15| 

is.  V 

20| 

20J 

21* 

15J 

IS' 

104 

204 

214 

\4_ 

18|- 

5I 

204 

124  SECTION  THREE 

Subtraction 
3.    Find  answers : 


A 

a.       4* 

B 

41 

c 
41t 

D 
31* 

E 

20* 

50* 

b.        ? 
+  36 

50* 

? 
+  36* 

50 

? 
+  36* 

50 

? 
+  30* 

50 

? 
+  19* 

501  5Ql  50  50  50 


4.    Subtract  191  from  100. 


PROCESS 

Say  ^  and  \  (writing  1)  are  1.     Carry- 
ing 1  to  9,  say  10  and  0  (writing  0)  are 
10.     Carrying  1  to  1,  say  2  and  8  (writing 
8)  are  10.     Test  by  adding  80^  and  19f 

100 
19| 

801 

Am. 

5.    Subtract  : 

A 

B 

c 

D 

E 

a. 
b. 
c. 
d. 

80 
-19* 

75* 
-48* 

93* 
-57 

62 
-13* 

48* 
-29 

-281 

471 

*•  2 

-19 

-S* 

44* 
-16* 

63 
-14* 

-22 

62 

73* 
-25* 

84* 
-46 

72* 
-261 

95 
-59* 

861 
-38* 

77* 
-49 

68 
-19* 

50J 
-23 

REDUCTIONS  125 


Halves  and  Fourths 
Preparatory  Exercises 
i.    How  many  quar-     . 


ters  in  1  quarter  and  1    \ 
quarter?  -i 

2.    What  single  piece   ^— 
of  money  has  the  same  L 

value  as  2  quarter  dol-    / — * 
lars?  ^— 


3.  What  fraction  has  the  same  value  as  |-? 

NOTE.  When  f  is  changed  to  ^-,  it  is  expressed  in  lowest 
terms. 

4.  How  many  fourths  are  3  fourths  and  1  fourth  ? 

5.  Give  the  sum  of  -|-  + 1  as  a  whole  number. 

Improper  Fractions.     Mixed  Numbers 

ib  f  9  f  9  % 9  are  called  proper  fractions,  since  each  is 
less  than  1. 

•|,  f?  f  >  V~>  are  called  improper  fractions,  since  each 
is  1  or  more. 

2^-,  3^,  ?•§-,  are  called  mixed  numbers,  since  each 
consists  of  a  whole  number  and  a  fraction. 

6.  Change  each  of  the  following  improper  fractions 
to  a  whole  number  or  to  a  mixed  number : 

a.   f .  6.    |.  c.    J.  rf.   f. 

e.    f  /    f.  jr.    f .  h.   |. 

7.  How  many  dollars   are  (a)  4   quarter-dollars  ? 
(6)  4  half-dollars  ?     (c)  6  half-dollars  ? 


126  SECTION  THREE 

Addition 

8.  Find  the  sum  (a)  of  38J-  and  271.  (6)  Of  38J 
and  271   (c)  Of  38f  and  271.  (d)  Of  38f  and  27f  . 

a.   38J    i,   381    c.   38|    d.   38f 

+  271  +27i  -h27i  +  27f 


Ans.  65J         Ans.  65f        Ans.  66J         Ans.  66j 

In  (a)  the  sum  of  the  fractions  is  f.  Change  |-  to 
^  and  write  \  under  the  fractions.  Add  the  whole 
numbers. 

In  (6)  change  \  to  {•  and  add  to  J.  Write  the  sum, 
|-,  under  the  fractions  ;  etc. 

In  (c)  change  \  to  \  and  add  to  f,  making  |-,  which 
is  equal  to  1£.  Write  ^  under  the  fractions  and  carry 
1  to  the  whole  numbers. 

In  (d)  change  the  sum  of  the  fractions  |-  to  1|^, 
which  is  equal  to  1J.  Write  J  under  the  fractions 
and  carry  1  to  the  whole  numbers. 

Sight  Exercises 
NOTE.     Change  |  in  a  result  to  \. 

Give  sums  : 

A  B  C  D  E 

a.       31  31  4f  If  3J 

+  31          +3J-  +51  +1|  +6j 

&•        li  2i  2J  3}  31 

li  3f  21  2  31 

li  4  2J  If  31 


SUBTRACTION  OF  MIXED  NUMBERS  127 

Written  Exercises 

Add  the  following : 

A  B  CD 

a.    131  6J  20}  7J 


3} 

16J- 

8J 

29 

9J 

25 

261 

a 

501 

231 

b.    53} 

271 

53} 
271 

651 

48| 
291 

48} 
291 

Sight 

Give  answers  : 

Exercises 

A 

B 

c 

D 

E 

a.    16J 

-4 

24} 

-M 

33} 

-It 

501 

b.   291 

38} 

0  1 

~*       1?" 

42} 

35 

46 

c.   28 
'-I* 

36 

47 

xrcl 
OO^ 

631 

Subtract  : 

Written 

Exercises 

A 

5 

C 

D       ' 

E 

a.   38} 
-19J 

62}            95} 
-331        -27} 

65} 
-16J 

46 
-17J 

b.    73 
-25£ 

84 
-36J 

50 

29-2- 

57} 

-28J 

128  SECTION  THREE 

— _ 

Oral  Problems 

1.  If  I  buy  goods  amounting  to  $  1 J,  how  much 
change  should  I  get  out  of  a  $  10  bill  ? 

2.  A  grocer  sold  1J  pounds  of  black  tea  and  f 
pound  of  green  tea.     How  many  pounds  did  he  sell 
of  both? 

3.  At  $  1^-  each,  what  is  the  cost  of  3   baseball 
gloves  ? 

4.  If  I   have  6  yards  of  calico  and   I  use  three 
fourths  of  a  yard,  how  much  have  I  left  ? 

5.  A  baker  has  3J  apple  pies  and  4J-  peach  pies. 
How  many  has  he  of  both  kinds  ? 

6.  One  cow  gave  15  \  quarts  of  milk  and  another 
gave  16^  quarts.     How  many  quarts  did  both  cows 


give? 


Written  Problems 


1.  If  I  buy  goods  amounting  to  $  19J,  how  much 
change  should  I  receive  out  of  a  $  50  bill  ? 

2.  A  grocer  sold  in  a  day  24 \  pounds  of  black  tea 
and  18|-  pounds  of  green  tea.     How  many  pounds 
did  he  sell  of  both? 

3.  At  $  17J  each,  what  is  the  cost  of  4  tables  ? 

4.  If  I  have  60  yards  of  muslin,  how  many  yards 
shall  I  have  after  using  13 J  yards? 

5.  A  dealer  has  23 \  apple  pies,  14J  peach  pies,  and 
3£  plum  pies.     How  many  pies  has  he  ? 


ADDITION  OF  MIXED  NUMBERS  129 

Thirds  and  Sixths 
Preparatory  Exercises 
i.    How  many  halves     1 


in  1  ?  How  many  thirds  \ __ 

in  1  ?  How  many  sixths  -i  JL 


in  1  ?  /  ^  \  / 

1.11     _L     •  \T  7*-*  . 

2.    How  many  sixths 
in  one  half?  How  many  /~ 
sixths    in    one    third? 
How   many   sixths    in 
two  thirds?  \I 


3.  How  many  sixths  in  1  sixth  + 1  sixth  ?     How 
many  thirds? 

4.  How  many  sixths  in  1  sixth  +  1  third  ?     Give 
the  sum  of  ^  4-  ^  in  lowest  terms. 

5.  How  many  sixths  in  1  sixth  +  1  half?     Give 
the  sum  of  J  +  \  in  lowest  terms. 

Sight  Exercises 

Give  sums.     Change  f  in  a  result  to  J,  f  to  J,  J 
tof. 

A  B  C  D  E  F 

a.    IJ  21         '31  4f  51  6» 

!i  2J  3J-  4J  5J  6J 

6.  71     8|     9f     8f     7f     6| 
"J-     8J     91     8f     7J     6J 


130  SECTION  THREE 

Written  Exercises 


Add: 

A 

B 

C 

D 

a. 

281 

28| 

28* 

28* 

8* 

8f 

/  8* 

8  - 

191 

19$ 

1Q1 

LJG 

19* 

1}. 

27* 

381 

4 

39| 

32 

7* 

661 

50 

5* 

43 

25* 

4* 

c. 

16* 

33* 

11* 

62| 

22| 

8* 

38 

351 

39 

14* 

46f 

1* 

d. 

45J 

24* 

571 

14* 

181 

58J 

-lO"o" 

95 

24* 

7* 

18| 

49 

e. 

47* 

26 

36f 

46| 

37 

7§ 

5f 

15| 

8* 

59f 

28| 

8| 

f. 

29* 

8* 

651 

43 

35* 

681 

17 

38* 

14* 

9i 

3| 

5* 

'- 

g. 

34f 

28 

641 

28J 

24f 

41* 

5* 

8* 

34 

19| 

25* 

48 

SUBTRACTION  OF  MIXED  NUMBERS 
Sight  Exercises 


131 


Subtract  : 

A 

D                                /"? 

Jj                             L/ 

D 

£                F 

a.   2 

a 

9                 ^1 
3 

11               11 
6                    6 

H 

41           6 

4.1               re  2 
^F              °¥ 

b.    7f 

li 

11          ii 

3                       2 

8             61 

Subtract  : 

Written 

Exercises 

A 

B 

C 

z> 

a.   75 

94 

87 

93 

13J 

b.   46} 

26} 

32} 

18J 

41} 

27J 

52J 
38| 

65 

48J 

57f 

674 

54| 

c.    70J 
43J 

d.   33$ 
16J 

82| 

901 
37J 

41} 

IZi 

82 

68J 
29J 

70 

e.   53 

26J 

80i 

18f 

58J 

'S 

72} 

49i 

61| 

132  SECTION  THREE 

Ratio 
Oral  Problems 

1.  What  part  of  a  dozen  (a)  is  2  ?  (&)  3  ?  (c)  4  ? 
(d)  6? 

2.  If  a  dozen  oranges  cost  18  cents,  what  is  the 
cost  (a)  of  a  half  dozen  ?    (&)  Of  J-  dozen  ?    (c)  Of  £ 
dozen  ? 

3.  At  3  peaches  for  5  cents,  (a)  find  the  cost  of 
6   peaches.      (6)    Of   9   peaches,      (c)    Of   a  dozen 
peaches. 

4.  If  3  men  can  do  a  piece  of  work  in  20  days, 
how  long  would  it  take  6  men  to  do  the  same  work  ? 

5.  How  many  men  can  do  in  10  days  a  piece  of 
work  that  requires  5  men  for  20  days  ? 

6.  At  the  rate  of  20  pages  in  3  days,  how  long 
would  it  take  to  finish  100  pages  ? 

7.  If  2  fifths  of  a  number  is  40,  what  is  4  fifths 
vof  the  number? 

s.  When  bricks  sell  for  $  7  a  thousand,  what  is 
the  cost  of  7,000  bricks  ? 

9.  At  3  for  2  cents,  find  the  cost  of  60  news- 
papers. 

10.  When  a  6-acre  field  produces  100  bushels  of 
wheat,  what  should  a  3 6-acre   field   produce  at  the 
same  rate  ? 

11.  At  the  rate  of  40  miles  in  3  hours,  how  long 
should  it  take  a  freight  train  to  go  160  miles? 


ADDITION  AND  SUBTRACTION  133 

Fifths 

Sight  Exercises 
i.    Give  answers : 

A  B  C  D  E 

a.       4*  3f  5*  8f          9* 

6f          +2f       +  3£ 


6.       9*  :  ' 

8t 

fi2                     fil 

U"F"                                \J"F" 

5                        5 

-4J         -2 

5 

e.        6 

7 

8               9 

8 

-If 

-If 

-  1*         -  8f 

-7f 

2.    Add: 

Written 

Exercises 

A 

B 

C 

D 

a.    19f 
20J 

I.   59f 

28| 

51 

3 

35f 

18 

ie| 

36f 

71 

48f 

3 

59f 
29* 

3.    Subtract  : 

A 

B 

C 

D 

a.        40 

51 

62 

73 

-16* 

-25f 

-37f 

-58* 

b.       84* 
-37f 

95f 
-69J 

86f 
-57* 

77* 
-59 

134  SECTION  THREE 

Oral  Review  Problems 

1.  Grace  weighs    64    pounds,   and    her    brother 
weighs   36    pounds  more  than  Grace.     How  many 
pounds  do  both  weigh  together? 

2.  How  much  less  than  a  dollar  has  a  boy  who  has 
a  half  dollar,  a  quarter,  a  dime,  a  nickel,  and  a  cent  ? 

'  3.    How  many  pounds  are  there  in  3  loads  of  hay 
weighing  21  hundred  pounds  each  ? 

s  >/  4.   How   many  seats  are  there  in  8   classrooms 
containing  40  seats  each? 

5.  How  many  pounds  are  there  in  320  ounces  ? 

6.  Change  2  feet  9  inches  to  inches. 

7.  In   a   school   of    480   pupils,  one  sixth  were 
absent  on  a  stormy  day.     How  many  were  present  ? 

8.  How  many  feet  of  wire  netting  will  inclose  a 
plot  31  feet  wide,  100  feet  long? 

9.  At  10  cents  each,  how  much  fare  is  received  from 
64  passengers  ?     How  much  fare  at  5  cents  each  ? 

10.  Mark  has  read  50  pages  in  a  book  and  there  are 
still  32  to  read.  How  many  pages  are  there  in  the  book  ? 

11.  An  airship  sailed  2  hours  45  minutes.     How 
many  minutes  less  than  3  hours  was  it  in  the  air  ? 

12.  How  many  weeks  are  there  in  350  days  ?     How 
many  weeks  and  days  are  there  in  355  days  ? 

is.    How  many  half-pint  cups  are  there  in  2  quarts  ? 
14.    How  many  days  are   there   in   the   last   two 
months  of  the  year  ? 


REVIEWS 


135 


is.  At  1J  bushels  per  acre,  how  many  bushels  of 
wheat  are  required  to  sow  40  acres  ? 

is.  When  wool  loses  ^  of  its  weight  in  washing, 
what  will  a  quantity  of  wool  weigh  after  washing  if 
it  weighs  80  pounds  before  it  is  washed  ? 

17.  When  oats  weigh  32  pounds  per  bushel,  what 
is  the  weight  of  a  peck  of  oats  ? 

is.  At  the  rate  of  40  cents  for  \  yard,  how  many 
yards  of  silk  can  be  bought  for  $  2.40  ? 

19.  (a)  How  many  feet  of  ribbon  are  required  for 
30  bows,  when  each  bow  takes  24  inches  ?     (b)  How 
many  yards  ? 

20.  At  ^  cent  a  pound,  how  many  pounds  of  cotton 
must  a  man  pick  to  earn  (a)  $  1  ?  (6)  $  2J  ? 

21.  At  12  miles  per  hour,   (a)  how  many  hours 
does  an  automobile  take  to  go  480  miles  ?     (&)  How 
many  days  of  10  hours  each  ? 

22.  0)    What  part  of  63  is  21  ? 
63  is  42  ? 

23.  A  boy  had  a  trip  of  120 
miles  to  make.     How  many  miles 
remained  after  he  had  gone  f  of 
the  distance  ? 

24.  What  is  the  perimeter  of  a 
triangle  when  each  of  the  three 
equal  sides  measures  21  inches? 

25.  What  is  the  fare  for  124  miles  at  2  cents  per  mile  ? 


(&)  What  part  of 


21  in. 


21  in. 


21  in. 


136  SECTION   THREE 

26.  At  20  quarts  of  gasoline  a  day,  how  many  gal- 
lons will  a  motor  boat  use  in  10  days  ? 

27.  A  boy  set  out  360  plants,  of  which  J  died. 
How  many  remained  ? 

28.  How  many  eggs  are   there  in  a  box  of  30 
dozen  ? 

29.  A  man  weighs  150  pounds  and  his  son  weighs 
50  pounds  less.     How  many  pounds  do  both  together 
weigh  ? 

so.    How  much  more  than  $  15  is  the  cost  of  eight 
barrels  of  apples  at  $2|-  per  barrel  ? 

31.  What  day  of  the  year  is  (a)  Feb.  1  ?     (&)  March 
1,  1915  ?     (c)  March  1,  1916  ? 

32.  How  many  passengers  at  5  cents  each  will  pay 
$  1.50  in  fares  ? 

33.  On  one  trip  a  conductor  collected  5  cents  each 
from  8  passengers  and  3  cents  each  from  10  passen- 
gers ;  how  much  did  he  collect  on  that  trip  ? 

34.  A  conductor  collected  on  one  trip  $  1.30  in  fares,' 
20  of  them  being  5-cent  fares  and  the  remainder  3- 
cent  fares.     How  many  were  3-cent  fares  ? 

35.  How  many  eggs  are  there  in  3^  dozen  ? 

36.  What  is  the  cost  of  4  horses  at  $200  each  ? 

37.  How  much  less  than  $500  will  be  the  cost  of 
8  cows  at  $50  each? 

38.  How  much  more  than  $500  will  be  the  cost  of 
11  cows  at  $50  each? 


WRITTEN  REVIEWS  137 

Written  Review  Problems 

1.  A  boy  weighs  96  pounds,  and  his  father  weighs 
75  pounds  more  than  the  son.     What  is  the  total 
weight  of  the  two? 

2.  How  much  less  than  1.0  dollars  has  a  man  who 
has  a  $  5  bill,  $  2  bill,  $  1  bill,  a  silver  dollar,  a  half 
dollar,  a  quarter,  a  dime,  a  nickel,  and  a  cent  ? 

3.  Find  the  weight  of  2  loads  of  hay  weighing 
1,975  pounds  each. 

4.  How  many  seats  are  there  in  16  class  rooms 
each  containing  40  seats  ? 

5.  How  many  pounds  are  there  in  496  ounces  ? 

6.  Change  15  feet  9  inches  to  inches. 

7.  In  a  school  of  475  pupils,  two  fifths  of  them 
were  unable  to  reach  school  on  a  very  stormy  day. 
How  many  were  present? 

8.  How  many  feet  of  wire  netting  will  inclose  a 
plot  40  feet  wide,  140  feet  long  ? 

9.  At  5  cents   each  how   much  fare  is  received 
from  97  passengers  ? 

10.  Flora  has  read  147  pages  in  a  book  and  has 
still  154  pages  to  read.     How  many  pages  are  there 
in  the  book  ? 

11.  An  airship  sailed  1  hour  37  minutes.     How 
many  minutes  longer  should  it  have  sailed  to  remain 
in  the  air  (a)  2  hours  ?     (b)  3  hours  ? 

12.  How  many  weeks  and  days  in  400  days? 


138  SECTION  THREE 

13.  How  many  quarter  pint  cups  are  there  in  8 
gallons  ? 

14.  How   many   days   are   there  in   the   last   six 
months  of  the  year? 

is.   At  1J  bushels  per  acre  how  many  bushels  of 
wheat  are  required  to  sow  48  acres  ? 

16.  When  raw  silk  loses  £  of  its  weight  in  boiling, 
what  will  be  the  weight  after  boiling  of  a  quantity 
that  weighs  96  pounds  before  it  is  boiled  ? 

17.  What  is  the  weight  of  a  half  peck  of  corn  at 
the  rate  of  56  pounds  to  the  bushel  ? 

is.    If  corn  is  bought  at  the  rate  of  15  cents  a  peck, 
how  many  bushels  can  be  bought  for  $21.60  ? 

19.  How  many  yards  of  ribbon  are  required  for  36 
bows,  if  each  bow  takes  21  inches? 

20.  At  \  cent  per  pound,  how  many  pounds  of 
cotton  must  a  man  pick  to  earn  $  13.86  \ 

21.  At  12  miles  per  hour,  how  many  days  of  8 
hours  each  will  it  take  an  automobile  to  go  480  miles  ? 

22.  (a)  What  part  of  120  is  24  ?     (6)  What  part 
of  120  is  72  ?     (c)  What  part  of  120  is  96  ? 

23.  A  boy  had  a  journey  of  120  miles  to  make. 
How  many  miles  remained  after  he  had  finished  J  of 
the  distance  ? 

24.  Find  the  perimeter  of  a  square  if  each  of  the 
4  equal  sides  measures  13 \  inches. 

25.  What  is  the  fare  for  124  miles  at  2J^  per  mile  ? 


WRITTEN  REVIEWS  139 

26.  At  25  quarts  of  gasoline  per  day  how  many 
gallons  will  a  motor  boat  use  in  32  days  ? 

27.  A  man  set  out  396  cabbage  plants,  -^j-  of  which 
died.     How  many  remained  ? 

28.  How  many  eggs  are  there  in  6  boxes  of  30 
dozen  each  ? 

29.  A  man  weighs  153  pounds,  and  his  son  weighs 
58  pounds  less.     What  is  the  total  weight  of  both  ? 

so.    How  much  more  than  $  15  is  the  cost  of  8 
barrels  of  apples  at  $2.75  per  barrel? 

31.  What    day    of    the    year    is    (a)    Feb.    22? 
(6)  March  4,  1915?     (c)  May  30,  1916?     (d)  July 
4,  1917? 

32.  How  many  passengers  at  5  cents  each  will  pay 
$2.45  in  fares? 

33.  On  one  trip  a  conductor  received  5  cents  each 
from  21  passengers  and  3  cents  each  from  13  passen- 
gers ;  what  was  the  total  amount  received  on  that  trip  ? 

34.  A    conductor    collected    altogether    $  1.50    in 
fares,  24  of  them  being  5-cent  fares  and  the  remainder 
3-cent  fares.     How  many  3-cent  fares  were  there  ? 

35.  How  many  eggs  are  there  in  9J  dozen  ? 

36.  What  is  the  cost  of  5  horses  at  $  175  each? 

37.  How  much  less  than  $  500  will  be  the  cost  of 
7  cows  at  $  55  each  ? 

38.  How  much  more  than  $  500  will  be  the  cost  of 
11  cows  at  $55  each? 


140  SECTION  THREE 


Addition  and  Subtraction 
Sight  Drills 

1.  Add  75  to  each  of  the  following  numbers  : 

A        B        C        D        E        F        G         H        I         J 

a.  26  74  48  59  99  18  36  69  .95  49 

6.  83  19  15  46  96  74  28  66  15  56 

c.  47  35  84  26  78  89  57  86  77  38 

d.  65  58  37  45  39  55  29  68  92  87 

e.  94  27  93  67  85  75  97  16  88  79 

2.  Subtract  each  of  the  foregoing  numbers  from 
120. 

3.  Add  350  to  each  of  the  following  numbers : 


A 

B 

C 

D 

E 

F 

a. 

90 

120 

35 

105 

2300 

900 

b. 

70 

210 

46 

206 

3400 

800 

c. 

50 

130 

18 

307 

4500 

700 

d. 

80 

320 

27 

408 

5600 

640 

e. 

60 

440 

39 

509 

6200 

530 

4.   Give  answers  rapidly : 
Think  121  +  50  +  6.         Think  121  -  50  -  6. 


A 

B 

c 

a. 

121  +  56 

122-63 

162  +  84 

b. 

121-56 

140  +  51 

162-84 

c. 

134  +  45 

140-51 

173  +  75 

d. 

134-45 

151+62 

173-75 

e. 

122  +  63 

151-62 

184  +  22 

WRITTEN   REVIEWS 


141 


Addition  and  Subtraction 


Written  Exercises 


i.   Add.     Test 


A 

B 

c 

D 

a.   43,875 

62,776 

48,256 

2,862 

2,250 

2,342 

38,451 

2,473 

8,429 

5,419 

4,836 

52,813 

885 

763 

629 

694 

9,680 

8,274 

985 

4,178 

b.    13,336 

12,643 

84,195 

47,386 

4,236 

656 

464 

7,562 

48,512 

5,472 

7,358 

3,625 

4,087 

58,688 

969 

10,533 

6,472 

4,865 

4,272 

8,524 

c.    15,625 

12,075 

4,524 

58,498 

7,405 

4,437 

7,525 

4,295 

964 

43,949 

61,329 

14,868 

38,228 

5,350 

2,316 

5,564 

2,545 

9,527 

6,395 

9,040 

21,864 

20,685 

4,567 

6,977 

2.    Subtract. 

Test  by  adding  upward  : 

a.   90,000 

83,210 

75,634 

62,350 

7,086 

75,065 

9,876 

48,907 

6.   90,090 

80,000 

70,700 

60,000 

83,956 

1,234 

36,895 

5,080 

142 

SECTION 

THREE 

3. 

Add: 

A 

B 

C 

a. 

$123.45 

$907.48 

$  680.70 

67.98 

35.06 

90.00 

76.59 

243.65 

77.96 

803.20 

76.78 

40.90 

47.00 

90.12 

465.58 

59.83 

83.75 

69.49 

6. 

$316.25 

$949.34 

$469.00 

57.42 

73.44 

74.05 

54.58 

750.27 

526.51 

602.72 

46.81 

57.36 

59.50 

245.54 

425.83 

35.00 

382.28 

35.10 

c. 

$537.46 

$456.56 

$    63.42 

45.91 

346.21 

633.31 

48.91 

86.90 

678.92 

756.84 

27.64 

87.14 

88.00 

78.04 

694.00 

68.27 

215.84 

318.25 

4. 

Subtract  : 

A 

B 

c 

a. 

$385.34 

$472.80 

$316.25 

198.76 

73.86 

158.87 

6. 

$907.48 

$  680.70 

$469.00 

244.65 

465.58 

74.05 

D 

159.24 

984.85 

76.54 

59.00 

266.13 

29.32 

.  52.63 
265.76 

83.74 
801.82 
724.00 

96.98 

;  37.42 
862.00 
375.89 
92.66 
348.15 
438.56 


D 
123.45 

67.89 

801.82 

724.98 


i. 


DRILL  EXERCISES 

Multiplication  and  Division 

Drill  Exercises 
Give  products  : 


143 


^4 

B 

c 

D 

E 

a. 

2x 

20 

3x20 

4x20 

5x20 

2 

x91 

6. 

2x 

30 

3x30 

4x30 

5x30 

3 

x81 

c. 

2x 

40 

3x40 

4x40 

5x40 

4 

x71 

d. 

2x 

50 

3x50 

4x50 

5x50 

5 

x61 

e. 

2x 

60 

3x60 

4x60 

5x60 

6 

x51 

/. 

2x 

70 

3x70 

4x70 

5x70 

7 

x41 

F 

G 

H 

7 

j 

a. 

6x 

20 

7x20 

8x20 

9x20 

2 

x21 

I. 

6x 

30 

7x30 

8x30 

9x30 

3 

x31 

c. 

6x 

40 

7x40 

8x40 

9x40 

4 

x41 

d. 

6x 

50 

7x50 

8x50 

9x50 

5x51 

e. 

6x 

60 

7x60 

8x60 

9x60 

6 

x61 

f- 

6x 

70 

7x70 

8x70 

9x70 

7 

x71 

2. 

Give  quotients  : 

A 

B 

C 

D 

E 

a. 

30 

)270 

40)280 

50)450 

60)480 

20 

)160 

6. 

70 

)350 

80)480 

90)810 

20)180 

30 

)180 

C. 

80 

)720 

70)630 

60)540 

50)300 

40 

)360 

A 

40 

)320 

30)240 

20)160 

30)180 

50)250 

e. 

50 

)350 

70)490 

90)630 

80)560 

60 

)360 

/ 

60 

)420 

40)360 

30)210 

50)400 

70 

)280 

144  SECTION  THREE 

Oral  Problems 

fy.  /    i.   How  many  farms  of  80  acres  each  can  be  made 
•'  from  640  acres  of  land  ? 

-  /  2.    How  much  would  be  received  for  9  cows,  if 
they  were  sold  at  $50  each? 

3.  A  man  bought  a  lot  for  6  hundred  dollars,  and 
built   a   house   costing    18    hundred    dollars.     How 
many  hundred  dollars  did  both  cost  ? 

4.  A  cord  of  wood  contains  128  cubic  feet.     How 
many  cubic  feet  are  there  (a)  in  ^  cord?     (6)  In  \ 
cord? 

5.  From  a  box  containing  30  dozen  eggs,  200  eggs 
were  sold.     How  many  remained  ? 

6.  If  a  man  works  309  days  in  a  year,  how  much 
does  he  earn,  at  the  rate  of  $  3  per  day  ? 

7.  How  many  cubic  inches  are  there  in  a  block  of 
stone  40  inches  long,  30  inches  wide,  4  inches  thick  ? 

8.  At  60  firecrackers   to   the   pack,  how  many 
packs  contain  540  firecrackers? 

9.  What  is  the  cost  of  480  pounds  of  butter  at  J 
dollar  per  pound  ? 

10.  If  21  men   require  32  days  to  do  a  piece  of 
work,  (a)  what  part  of  this  time  should  it  take  84 
men  to  do  the  same  work  ?     (6)    How  many  days  ? 

11.  A  dealer  received    $32   each   for   3    suits   of 
clothes.     How  much  less  than  $  100  did  he  receive 
for  them  ? 


MULTIPLICATION  AND  DIVISION  145 

Multiplying  and  Dividing  by  11 
Oral  Exercises 

1.  Count  by  ll's  from  11  to  132. 

2.  How  many  are  (d)  two  ll's?     (b)  Eleven  2's? 
(c)   Three  ll's?      (d)  Eleven  3's?      (e)  Four  ll's? 
(/)    Eleven    4's     (g}    Five   ll's?     (h)    Eleven   5's? 
(i)  Six  ll's?     (j)  Eleven  6's?     (k)  Seven  ll's?     (7) 
Eleven  7's?     (m)  Eight  ll's?     (n)  Eleven  8's?     (o) 
Nine  ll's?     (p)  Eleven  9's? 

Written  Exercises 

1.  Multiply  by  11: 

A 

a.  Ill 

b.  666 

c.  765 

d.  454 

2.  Divide  by  11 : 

A                  B                  C  D 

a.  1,210  1,342  1,595  1,859 

b.  2,761  3,949  5,423  7,403 

c.  9,119  8,712  7,260  5,808 

3.  Divide  by  11.     Find  quotients  and  remainders: 

A  B  C  D 

a.  3,681  8,937  9,432  9,004 

b.  3,700  9,000  8,400  6,700 


B 

c 

D 

E 

222 

333 

444 

555 

777 

888 

909 

876 

654 

543 

432 

321 

565 

787 

898 

579 

146  SECTION  THREE 

Multiplying  and  Dividing  by  12 

Learn  the  following  table : 

12  times  1  are  12  12  times    7  are    84 

12  times  2  are  24  12  times    8  are    96 

12  times  3  are  36  12  times    9  are  108 

12  times  4  are  48  12  times  10  are  120 

12  times  5  are  60  12  times  11  are  132 

12  times  6  are  72  12  times  12  are  144 

Oral  Exercises 

1.  How  many  inches  are  there  in  1 1  feet  ? 

2.  At  12  cents  per  yard,  what  is  paid  for  7  yards 
of  muslin  ? 

3.  How  many  cents. are  12  nickels? 

4.  How  many  eggs  are  there  in  8  dozen  ? 

5.  Find  the  number  of  square  inches  in  12  rows, 
each  containing  12  square  inches. 

6.  How  many  cents  are  there  in  a  dozen  dimes  ? 

7.  How   many  panes   of    glass   are    there   in   6 
windows,  each  containing  12  panes? 

8.  How  many  feet  are  there  in  12  yards  ? 

9.  How  many  years  are  there  in  60  months  ? 

10.  How  many  dimes  are  there  in  $  1.20  ? 

11.  How  many  inches  in  3  feet  6  inches  ? 

12.  How  many  years  and  months  in  40  months  ? 

13.  How  many  square  feet  are  there  in  a  plot  of 
ground  12  feet  square? 


MULTIPLICATION  AND  DIVISION  147 

Sight  Exercises 


Give  products  : 

A 

B                       C 

D 

a.    9x12 

12  x  8         20  x  12 

12x30 

b.   6x12 

12x5         12x40 

50x12 

c.    7x12 

12  x  4         60  x  12 

12x70 

d.   3x12 

12x2         12x80 

90x12 

Written  Exercises 

Multiply  by  12  : 

A 

BCD 

E 

a.    Ill 

222          333          444 

555 

b.   666 

777          818          729 

645 

c.    564 

765          654          543 

432 

d.   321 

454          565          787 

809 

Sight  Exercises 

Give  quotients 

i 

A 

D                                   /"* 

Jj                                   (_/ 

D 

a.    120  +  12 

96+12      360  +  12 

840  +  12 

b.    144  +  12 

48  +  12      600  +  12 

960  +  120 

c.    108+12 

60  +  12      840  +  12 

720  +  12 

d.    132  +  12 

84  +  12      480  +  12 

240  +  120 

Written  Exercises 

Divide  by  12  : 

A 

B                   C 

D 

a.    1,332 

1,572           1,620 

1,884 

b.   2,772 

3,948          5,424 

7,416 

c.    8,712 

9,180          8,580 

6,756 

d.   5,088 

3,384          4,500 

6,336 

148  SECTION  THREE 

Multipliers  containing  Ciphers 

Sight  Exercises 
Give  products  : 

A  B  C  D  E  F 

a.   21    32    11    22    33    23 
x400  x300  x50Q  x  400  x  300  x  300 

6.  2,100     3,200     1,100     2,200     3,200     2,200 
x4         x3         x5         x4         x3         x3 

c.   210   320    110    120    130   210 
x40   x30   x50   x40   x30   x  30 

Written  Exercises 
i.   Multiply  185  by  500. 


PROCESS 

The  product  by  0  ones  is  0;    write  0  in 
the  ones'  column.      The  product  by  0  tens 

rnrv  *  * 

is  0  ;    write  0  in  the  tens'  column.     Place 


92500  Ans.    the  right-hand  figure  of  the  product  by  5 
hundred  in  the  hundreds'  column. 


2.   Multiply: 

ABC 
a.   486x200  329x300  239x400 

6.    184x500  157x600  139x700 

c.  118x800  109x900  478x200 

d.  327x300  248x400  177x500 


MULTIPLICATION  149 

2.   Multiply  427  by  230. 


497  PROCESS 

The  product  by  0  ones  is  0;  write  0  in 
the  ones'  column.     Place  the  right-hand 


figure    of  the    product   by    3   under    3. 
854  Place  the  right-hand  figure  of  the  product 

98210  Ans.       by  2  under  2. 


ABC 

a.  475x210  309x320  217x430 

b.  175x520  146x63(0  128x740 

c.  119x830  105x950  337x250 

d.  209x360  208x470  170x580 

3.   Multiply  (a)  408  by  205  ;     (6)  205  by  408. 


(a)     408 
205 

PROCESS 

In  (a)  place  the 
right-hand  figure 
of  the  product  by 
5  in  the  ones'  col- 
umn.    Since  the 

(b)     205 
408 

2040 

1640 
8200 

83640  Ans. 

83640  Ans. 

product  by  0  tens 

is  0,  place  a  cipher  in  the  tens'  column.  Place  the  right- 
hand  figure  of  the  product  by  2  hundred  in  the  hundreds' 
column  of  the  same  line. 

ABC 

a.  102x806  108x907  207x405 

b.  203x409  305x306  506x108 

c.  389x205  473x205  309x309 


150  SECTION  THREE 

4.   Multiply  (a)  279  by  346;  (6)  346  by  279. 


PROCESS 

(a)  279  In  (a)  place  the  right-  (6)  346 

346  hand     figure     of    the  279 

product  by  6  under  6, 


"•"^    xi&iiu-xxo,uu.    iiguit,    Of  9400 

the  product  by  4  under 
837  4?   and   the    right-hand 


96534  Ans.   figure  of  the  product  by      96534   Ans. 

3  under  3. 

Test  (a)  by  multiplying  346  by  279,  as  in  (6).    If  the 
results  agree,  both  products  are  probably  correct. 


ABC 

a.  235x123  246x321  325x235 

b.  437x214  562x173  684x142 

c.  784x125  863x114  746x134 

d.  527  x 184  408  x  238  336  x  260 

e.  150x630  227x398  317x314 
/  208x407  638x156  416x239 
g.  356x249  256x349  583x158 
h.  475  x  206  567  x 146  900  x 106 
i.  136  x  634  678  x  135  760  x  130 
j.  235  x  389  786  x 127  508  x 103 
k.  480  x 108  890  x 1 12  326  x  275 
I  340  x  290  120  x  780  156  x  570 

w.  305x309  165x606  124x642 

n.  208x404  234x367  205x350 


LONG  DIVISION  151 

Long  Division 
Written  Exercises 

i.   Divide  58,376  by  99 ;  43,721  by  975 ;  68,374 
by  3,456. 


Ans.  589£ 

a 

PROCESS 

O                         ^  /i  i  o        yj  /j_  o  2i                                  /\  /yj  c*         1  vl  ~»  T  1  0 

Q                -xi/i/d.    rtT:  qiy  ?                   ^L/to*     -L  *^*i  4.  g  «' 

99)58376 
495 

975)43721            3456)68374 
3900                       3456 

887 
792 

4721                     33814 
3900                     31104 

956                     821                       2710 

Write  the  first  quotient  figure  over  the 
65       last  figure  of  the  first   partial   dividend. 
Write  a  quotient  figure  (or  a  cipher)  over 
each  remaining  figure  of  the  dividend. 

2.  Divide : 

A  B  C 

a.  8,058+102  54,324  +  108  86,785  +  1,021 

6.  9,315  +  405  41,814  +  207  93,472  +  2,032 

c.  9,178  +  706  65,178  +  306  96,736  +  3,023 

d.  9,911+901  90,720  +  405  93,288  +  4,056 

e.  7,308  +  812  88,704  +  504  90,126  +  5,007 
/.  9,824  +  614  96,480  +  603  96,496  +  6,031 
g.  9,545  +  415  98,982  +  702  98,308  +  7,022 
h.  9,592  +  218  96,360  +  803  96,420  +  8,035 


152  SECTION  THREE 


Oral  Exercises 

1.  At  20^  each,  how  many  articles  can  be  bought 
for 

ABODE 

a.   20^?       GO**?         100^?         HO**?       ISO/? 
6.    40/?       80/?         120^?         160/?       200 /? 

2.  At  19/  each,  how  many  articles  can  be  bought 
for 

a.   20^?       60/?         120^?         160^?       180X? 
6.    40^?      80^?        140^?         180^?      200^? 
and  how  many  cents  remain  in  each  case  ? 

3.  Give  the  number  of  articles  at  18  ^  each  that  can 
be  bought  for  each  of  the  following  sums,  and  state 
the  amount  remaining  in  each  : 

a.   40^        20^  100^  160  J*         180^ 

6.    80^         60  X  140^  120^        200^ 

4.  Give  quotients : 

A  B  CD 

a.   30)60  30)120  30)180  30)240 

6.    30)90  30)150  30)210  30)270 

5.  Give  quotients  and  remainders : 

a.  29)30  29)90  29)150  29)210 

6.  29)60  29)120  29)180  29)240 
c.   28)30          28)90            28)150          28)210 


DRILL  EXERCISES  153 

Long  Division 

Drill  Exercises 
Give  quotients : 

NOTE.    Omit  remainders,  if  any. 

A  B  CD 

a.   200)1,800     201)1,800     199)1,800  250)1,800 

6.   300)2,400     302)2,400     299)2,400  360)2,400 

c.  400)2,800     403)2,800     399)2,800  470)2,800 

d.  500)2,500     504)2,500     499)2,500  580)2,500 

e.  600)4,200      605)4,200     599)4,200  690)4,200 
/.   700)6,300     704)6,300     699)6,300  790)6,300 
g.  800)5,600      803)5,600     799)5,600  880)5,600 
h.   900)7,200     902)7,200     899)7,200  999)7,200 
t.   240)1,920     241)1,920     239)1,920  249)1,920 
j.   320)2,240     321)2,240     319)2,240  320)2,239 
k.   410)3,690     411)3,690     409)3,690  410)3,689 
I   520)2,080     521)2,080     519)2,080  520)2,076 

m.   630)3,780     631)3,780     629)3,780  630)3,774 

n.   710)4,970     711)4,970     709)4,970  710)4,953 

o.   820)4,100     821)4,100     819)4,100  820)4,096 

p.   910)8,190     911)8,190     909)8,190  910)8,183 


154  SECTION  THREE 

Oral  Problems 

1.  What  is  the  total  cost  of  a  lot  at  3  hundred 
dollars  and  a  house  at  21  hundred  dollars? 

2.  A  man  had  31  hundred  dollars  in  bank.     How 
much  remained  after  he  drew  out  8  hundred  dollars  ? 

3.  Give  the  cost  of  21  horses  at  $300  each. 

4.  A  driver  sold   30   cows  at  $41    each.     How 
much  did  he  receive  for  them  ? 

5.  At  4^  per  pound  what  is  the  cost  of  a  barrel  of 
sugar  containing  300  pounds? 

6.  How  many  20-acre  fields  are  there  in  a  farm 
of  640  acres  ? 

7.  At  20  bushels  to  the  acre  what  would  be  the 
yield  of  34  acres  of  wheat  ? 

8.  How  long  would   a  train  require   to  go  820 
miles  at  the  rate  of  41  miles  an  hour  ? 

9.  If   a  man  has  saved  $991,  how  much   more 
must  be  saved  to  have  $  1,000  ? 

10.  How 'many  square  yards  are  there  in  a  plot  of 
ground  32  yards  long,  30  yards  wide  ? 

11.  Mr.  Payne  has  two  farms,  one  of  260  acres  and 
the  other  of  120  acres.     How  many  acres  are  there 
in  both  ? 

12.  If  3  men  can  do  a  piece  of  work  in  21  days, 
how  long  would  it  require  1  man  to  do  it  ?     7  men  ? 

13.  How  much  shall  I  have  left  of  $  1,000  after 
paying  for  3  horses  at  $  300  each  ? 


WRITTEN  REVIEWS  155 

Written  Problems 

1.  What  is  the  total  cost  of  a  lot  at  $  375  and  a 
house  at  $  2,475  ? 

2.  A  man  had    $950  in  bank.     How  much  re- 
mained after  he  took  out  $  875.75  ? 

3.  Find  the  cost  of  21  horses  at  $375  each. 

4.  A  drover  sold  30  cows  at   $45  each.     How 
much  did  he  receive  for  them  ? 

5.  At  4^  per  pound  what  is  the  cost  of  a  barrel 
of  sugar  containing  375  pounds  ? 

6.  How  many  25-acre  plots  can  be  made  out  of 
600  acres  of  land  ? 

7.  At  19  bushels  to  the  acre  what  would  be  the 
yield  of  34  acres  of  wheat  ? 

8.  How  long  would  a  train  require  to  go  975 
miles  at  the  rate  of  30  miles  per  hour  ? 

9.  A  man  requires  $  1,000 ;  he  has  already  saved 
$  837.50.     How  much  does  he  still  need  ? 

10.  What  is  the  area  of  a  plot  of  ground  32  yards 
long,  29  yards  wide  ? 

11.  Mr.  Black  has  two  farms,  one  of  269J  acres  and 
the  other  of  1 10 \  acres.     How  much  land  is  there  in 
both? 

12.  If  3  men  can  do  a  piece  of  work  in  35  days, 
how  long  would  it  require  1  man  to  do  it  ?     7  men  ? 

13.  How  much  change  should  I  receive  out  of  a 
$1,000  bill  given  in  payment  for  3  horses  at  $317 
each? 


156  SECTION   THREE 

Written  Exercises 

In  dividing  969  by  19,  find  the  first  quotient  figure 
by  dividing  9  by  2,  19  being  nearly  20.     In  dividing 

975  by  39,  get  the  first  quotient  figure  by  dividing  9 
by  4. 

i.    Divide : 

A                          B  c 

a.  969-19  8,213-*- 191  61,280-*- 1,915 

b.  928-*- 29  9,376-293  82,124-*- 2,933 

c.  975-*- 39  9,480-*-395  86,922-*- 3,951 

d.  784-49  7,455-*- 497  89,496-*- 4,972 

e.  885-*- 59  8,386-*- 599  83,9 16-*- 5,994 
/    897-*- 69  8,376-*- 698  90,5 84-*- 6,9 68 
g.   869-4-79  6,368-*- 796  87,648-^-7,968 
h.   979-*- 89  9,834-*- 894  7 1,592-*- 8,949 

i.  891-*- 99  7,936-*- 992  69,489 -*- 9,927 

j.  704-88  9,691-*- 881  52,8 90-*- 8,8 15 

k.  936-*- 78  9,396-*- 783  70,497 -*- 7,833 

I  952-*- 68  9,590-*- 685  82,212-6,851 

m.  928-58  9,424-589  94,272 -*- 5,892 

n.  864-*-48  9,723-463  82,348-4,844 

o.  988-*- 38  9,650-*- 386  88,918-*- 3,866 

p.  952-28  9,690-285  99,960-2,856 

q.  936-18  9,752-184  95,836-1,843 

r.  945-*-27  9,936-276  99,432 -*- 2,762 

s.  999-37  9,672-*- 372  93,025-3,721 


ORAL   REVIEW  157 

Oral  Problems 

1.  How  many  ounces  are  there  in  3  pounds  ? 

2.  Change  50  ounces  to  pounds  and  ounces. 

3.  How  many  postage  stamps  are  there  in  a  sheet 
15  stamps  long,  3  stamps  wide  ? 

4.  What  is  the  cost  of  23  two-cent  stamps? 

5.  At  14  cents  a  gallon,  how  many  gallons  of  oil 
can  be  bought  for  42  cents  ? 

e.    If  45  men  require  30  days  to  do  a  piece  of  work, 
how  long  would  it  take  15  men  to  do  it? 

7.  At  16  bushels  to  the  acre,  how  many  acres  will 
produce  48  bushels  ? 

8.  Seven  times  8  are  how  many  more  than  50  ? 

9.  At  the  rate  of  15  examples  an  hour,  how  long 
does  it  require  a  girl  to  work  45  examples  ? 

10.  How  many  times  is  99  contained  in  100  ?  what 
is  the  remainder  ?     How  many  times  in  200  ?  what  is 
the  remainder  ?      In  300  ?    what  is  the  remainder  ? 
In  500  ?  what  is  the  remainder  ? 

11.  How  many  times  is  98  contained  in  100  ?  what 
is  the  remainder  ?     In  300  ?  what  is  the  remainder  ? 
In  700  ?  what  is  the  remainder  ? 

12.  At  99^  a  yard,  how  many  yards  of  silk  can  be 
bought  for  $  6,  and  how  many  cents  change  are  there  ? 

13.  A  girl  bought  7  yards  of  goods  at  99  ^  per  yard 
and  received  7^  change.     How  much  did  she  give  the 
storekeeper  ? 


158  SECTION  THREE 

Multiples  and  Factors 

Since  14  is  divisible  by  2  and  by  7,  it  is  a  multiple 
of  these  numbers ;  12  is  a  multiple  of  2,  of  3,  of  4, 
and  of  6. 

Since  14  is  divisible  by  2  and  by  7,  these  two  num- 
bers are  factors  of  14 ;  2,  3,  4,  and  6  are  factors  of  12. 

1  is  not  considered  a  factor  of  a  number,  neither  is  the 
number  itself. 

Oral  Exercises 

1.  What  number  will  exactly  divide  25  ?  49  ?  81  ? 
121? 

2.  What  two  numbers  will  exactly  divide  21  ?     26? 
33?     34?     35?     39?     46?     51?     55?     57? 

Prime  Numbers 

Since  they  have  no  factors,  1,  2,  3,  5,  etc.,  are  called 
prime  numbers. 

Sight  Exercises 

1.  Name  a  prime  number  between  6  and  9. 

2.  Name  two  prime  numbers  between  10  and  15. 
Two  between  16  and  20.     One  between  21  and  25. 
One  between  25  and  30. 

3.  Name  two  prime  numbers  between  30  and  40. 
Three  between  40  and  50.     Two  between  50  and  60. 
Two  between  60  and  70.     Three  between  70  and  80. 
Two  between  80  and  90.     One  between  90  and  100. 


FRACTIONS 


159 


Reduction 
Oral  Exercises 

When  a  thing  is  divided  into  8  equal  parts,  each 

part     is      called      an      T 

eighth,  written  -J.  <^  ~^||> 

i.  How  many  eighths  _L  x 

are  there  in  a  half  ?   In   / 
a   quarter?     In   three 


4 


fourths  ? 

2.    Change  to  8ths 


a. 


6. 


c.  f  . 


i    i 


In  the  fractions 


J,  J,  the  numbers  2,  4,  8,  are  called  the  denominators. 

In  the  fractions  J,  f,  -|,  •£,  the  numbers  1,  3,  5,  7, 
are  called  the  numerators. 

The  numerator  and  the  denominator  are  called  the 
terms  of  the  fraction. 

When  f  is  changed  to  J,  f  and  f  to  J,  f  to  f  ,  etc., 
each  fraction  is  changed  to  lowest  terms. 


3.    Change  to  lowest  terms  : 

ABC 


D 


E 


a.    i 

4  o  o  o  o 

b-    A  B"  6"  A  ta 

4.    Change  to  a  whole  or  to  a  mixed  number : 

ABODE 

«.  I          *         t         ¥         ¥ 


160  SECTION   THREE 

Adding  and  Subtracting  Fractions 
Preparatory  Exercises 

To  add  or  to  subtract  fractions  having  different 
denominators,  the  denominators  must  be  made  the 
same ;  that  is,  the  fractions  must  have  a  common  de- 
nominator. 

1.  Add ^  and  J.    What  is  the  common  denominator? 

2.  Add  i-  and  ^.    What  is  the  common  denominator  ? 

Zi  D 

3.  (a)  What  is  the  common  denominator  of  -|-,  ^, 
andi?     (6)  Ofi,i,andJ?     (c)  Of^andi?     (d)  Of 

?     (e)    Of  J  and*?     (/)    Of  1  J,  andj? 


Sight  Exercises 
Give  answers : 


A 

5 

c 

D             E 

F 

e 

a. 

J 

J 

i 

\       i 

1 

3 

4 

±i 

+  J- 

±i 

+1     +1 

±i 

+  | 

6. 

11    ' 

1* 

11 

14         11 

*»             A4 

if 

If 

±i 

±i 

+* 

+  |           +| 

+4 

+  1 

c. 

n 

if 

4 

1J             If 

if 

If 

±1 

±1 

+1 

+  f           +f 

+J 

+  1 

d      2J         2|         2|         2J         21         2f         2| 

±i     ±i     ±i     ±i     ±1     ±1     ±i 

e.      I  1  1  1  11         1J         If 


MIXED   NUMBERS  161 

Adding  Mixed  Numbers 
Sight  Problems 

1.  How  much  cloth  is  needed  for  a  suit  of  clothes 
if  4  yards  are  needed  for  the  coat,  1^  yards  for  the 
vest,  and  21  yards  for  the  trousers  ? 

2.  How  many  inches  (a)  in  ^  foot  ?     (6)  In  J-  foot  ? 
(c)  In  l  ft.  +  l  ft.?     (d)   What  part  of  a  foot  is  6 
inches  ?     (e)  What  part  of  a  foot  is  J  ft.  +  J  ft.  ?  t 

3.  (a)  What  is  the  smallest  number  that  is  divisible 
by  3,  by  4,  and  by  6  ?     (6)  What  is  the  least  common 
denominator  of  ^,  ^,  and  £?     (c)   How  many  12ths 
in   the   sum   of  J,  J,  and  J?      (d)  -|- 4- ^  +  J- =  how 
many  fourths  ? 

4.  After  a  man  had  sold  ^-  +  ^-  +  ^  of  his  farm,  («) 
what  part  of  his  farm  was  sold  ?     (6)  What  part  did 
he  still  own?     (c)  If  he  still  owned  40  acres,  how 
many  acres  did  he  own  at  first  ? 

Written  Exercises 

Add: 

ABODE 

a.  20|  16f  32  46|  72f 
13  7f  8J  4  20f 
_3|  1£_  19J-  Ji  _6_ 

6.  17J     30      14J     21f      8 
13      18J-      5J     16      22J 


162  SECTION   THREE 

Subtracting  Mixed  Numbers 
Oral  Problems 

1.  An  airship  remained  in  the  air  58-|   minutes. 
How  many  minutes  is  that  less  than  an  hour  ? 

2.  After  spending  \  and  J  of  his  money,  (a)  what 
part  of  his  money  did  a  boy  still  have?     (6)  If  he 
then  had  10  cents,  how  much  had  he  at  first? 

3.  A  man  had  to  walk  10  miles.     He  walks  3^ 
miles  the  first  hour  and  3 \  the  second  hour.     How 
many  miles  has  he  still  to  go  ? 

4.  Out  of  100  yards  of  cloth  921  yards  have  been 
used.     How  many  yards  remain  ? 

5.  How  much  more  than  $  50  will  be  the  cost  of 
a  dress  at  $  40 J  and  a  trunk  at  $  91  ? 

Written  Exercises 


Subtract  : 

A 

B 

c 

D 

E 

a.  30 

43 

74 

65 

72 

-18* 

-19J 

-27| 

-38* 

-47| 

6.  50 

83 

92 

36 

45 

-24* 

-46f 

-25* 

-16| 

-26* 

c.  30| 

42| 

51* 

62f 

71| 

-181 

-261 

-391 

-131 

-221 

MIXED   NUMBERS 


163 


Addition 

Written  Exercises 
i.  Find  the  sum  of  30f  +  25f  +  8f. 


PROCESS 

To  the  right  of  the  add- 
ends draw  a  vertical  line                QQJ^ 
and  from  its  top  draw  a                9_5 
horizontal     line.       Above 
the    latter   write   12   (the 

12 

9 
10 

8 

least    common    denonina-    Ans.    654-    -?4-  =  2  A  =  24- 

•fc         X  ^                 J_  £t                t 

tor).    Change  the  fractions 
to  ^-,  J-|,  and  -j^-,  respectively,  and  write  9,  10,  and  8  (the 
new  numerators)  under  12  (the  new  denominator).     Add 
these  numerators,  and  write  27  (their  sum),  over  12  (the 
common  denominator),  making  the  sum  of  the  fractions  f  -J  . 
Change  this  first  to  2^-,  and  then  to  1\.     Write  \  under 
the  original  fractions,  and  carry  2  to  the  whole  numbers. 

2.    Find  sums  : 
ABC 
30J             16|               5£ 
251              8J             201 
84-            394               84 

336 

60£ 
9f 

18f 
6 

3.   Add: 


2J 


20} 
Ji 


164  SECTION  THREE 

Addition  and  Subtraction 

Written  Exercises 

i.    A  field  contained  35^-  acres  of  land.     15}  acres 
were  sold.     How  much  remained  ? 


PROCESS 


Write  20  (the  least  common  de-  20 

nominator),    as    in    addition,    and 


35* 


3. 


18 
15 


18  and  15    (the   new   numerators). 
Place  3   (their  difference)  over  20  ±u  4 

(the  common    denominator),    mak-    Ans. 
ing  the  difference  between  the  frac- 
tions ^.     Write  the  latter  under  the  original  fractions, 
then  subtract  the  whole  numbers. 


2.    Subtract  : 

ABODE 

a.     15|  30f-          27£  54f  40} 

_8|         -14|         -9}         -261 


6.     64f  92f          87|  73f  50J 

-16f         -24J-       -59f 


3.    Find  answers  : 

a.     35|  35}          42|  42f  26| 

+  16f         -16f 


1.     26|  67|          67J 

_9  + 


c.     72J  72|          90f 

+  6|  -6f         +8f 


FRACTIONAL   PARTS  165 

Fractional  Parts  of  Numbers 
Oral  Exercises 

1.  How  many  ounces  (a)  in  J-  pound?     (&)  In  -f 
pound  ?     (c)  In  f  pound  ?     (d)  In  -J  pound  ? 

2.  Find  (a)  J-  of  24.     (6)  f  of  24.     (c)  f  of  24. 
(d)  %  of  24. 

3.  How  many  minutes  (a)  in  J-  hour?     (6)  In  f 
hour?     (c)  In  f  hour?     (d)  In  f  hour?     (e)  In  £ 
hour?     (/)  In   f   hour?     (^)  In   \    hour?     (A)  In 
1-  hour?     (i)  In  |  hour?     (j)  In  J  hour?     (£)  In 
|  hour? 

4.  How  many  hours  (a)  in  ^  day  ?     (6)  In  ^  day  ? 
(c)  In    i    day?     (d)  In    f    day?     (e)  In    f    day? 
(/)  In  l  day?     (g)  In  f  day?     (h)  In  f  day?     (i) 
In  I  day?     (j)  In  1  day?     (A:)  In  f  day? 

Sight  Exercises 


Give  answers  : 

A 

z?                             r* 

/->                                                     *-* 

D 

a. 

4 

of 

168 

J 

of 

184 

iof 

250 

\ 

of 

248 

1). 

i 

of 

366 

i 

of 

396 

Jof 

369 

i 

of 

648 

c. 

i 

of 

440 

i 

of 

484 

1  of 

4   01 

888 

I 

of 

848 

d. 

J 

of 

255 

J- 

of 

300 

j-of 

555 

J- 

of 

525 

e. 

I 

of 

606 

i 

of 

486 

Jof 

366 

i 

of 

420 

f. 

i 

of 

168 

i 

of 

248 

Jof 

328 

fr 

of 

480 

9- 

1 

of 

120 

1 

of 

120 

Jof 

150 

2 
S" 

of 

150 

h. 

] 

of 

150 

* 

of 

150 

|of 

180 

3 

of 

160 

166  SECTION   THREE 

Written  Problems 

i.   A  man  sold  -J  of  his  farm  of  168  acres.     How 
many  acres  did  he  sell  ? 


PROCESS 

Find  1  eighth  of  168 


by  dividing  168  by  8,    J  °f  Iff  A.  =  147  A.      Am. 

canceling  these  numbers,  and  writing  the  quotient  21, 
over  the  former.     Multiply  21  by  7  to  find  7  eighths. 


The  abbreviation  for  acres  is  A. ;  for  pounds,  Ib. ;  for  yards, 
yd. ;  for  miles,  mi. 

2.  How  many  pounds  are  there  in  f  of  a  ton  of 
2,000  pounds  ? 

3.  How  many  yards  are  there  in  J  mile,  a  mile 
containing  1,760  yards  ? 

4.  A  planter  sold  -f  of  his  crop  of  cotton  consisting 
of  258  bales.     How  many  bales  did  he  sell  ? 

5.  Of  a  grove  of  360  trees,  three  fifths  v  are  pine 
trees.     How  many  are  pine  trees  ? 

6.  How  far  has  a  train  gone  when  it  has  gone  f  of 
the  distance  from  New  York  to  Washington,  224  miles  ? 

7.  A  man  sold  for  |-  of  its  cost  a  farm  that  cost 
him  $  2,800.     What  did  he  receive  for  it  ? 

8.  An  acre  contains  160  square  rods.     How  many 
square  rods  are  there  in  a  plot  containing  |-  acre  ? 

9.  A   piece    of    cloth   contains    56    yards.     How 
many  yards  are  left  after  j-  of  the  piece  is  used  ? 


MIXED  NUMBERS  167 

Multiplying  by  a  Mixed  Number 
Preparatory  Exercises 

1.  If  a  horse  travels  at  the  rate  of  6  miles  an  hour, 
(a)  how  far  does  he  go  in  -|-  hour  ?     (6)  In  an  hour 
and  a  half  ? 

2.  How  many  miles  are  1J  times  6  miles  ? 

3.  At  12  cents  a  yard,  what  is  the  cost  (a)  of  2 
yards  of  muslin ?     (6)  Of  J  yard?     (c)  Of  2J  yards? 

4.  How  many  cents  are  2J  times  24  cents  ? 

5.  At  $  40  per  acre  what  is  the  cost  (a)  of  i  acre 
of  land  ?    (6)  Of  3i  acres  ? 

6.  How  many  dollars  are  3i  times  $  40  ? 

7.  How  many  bushels  of  oats  can  be  raised  (a)  on 
}  acre  at  the  rate  of  40  bushels  to  the  acre  ?     (&)  On 
If  acres? 

8.  How  many  bushels  are  If  times  40  bushels  ? 

Sight  Exercises 
Give  products : 

A  B  C  D          E          F 

a.        24          24          24          24          24         30 


6.        60          60          40          60          80         80 


c.       30          30          40          30          40         20 


168  SECTION  THREE 

Written  Exercises 


i.   A  man  makes  87  hats  in  a  week.     How  many 


will  he  make  in  2^  weeks  ? 


PROCESS  "7  nats 

Get  1  third  of  87  by  dividing  ?S 

87  by  3.  Place  the  right-hand  (i  times  87)  29 
figure  of  the  product  of  87  by  2  (2  times  87)  174 
in  the  ones'  column.  (2$-  times  87)  203  hats 


2.  Find  products.     Consider  the  mixed  number  the 
multiplier. 

A  B  c  D 

a.   86x21         84x31  96x21  34x41 

6.   88x4J-         75x5j  72x31  25  x  3£ 

c.    72x31        92x4J  84x51  48  x  2  J 

3.  Multiply  78  by  4f . 


78 

PROCESS  4JL 

First  find  |  of  78,  which  (J  of  78)     13 

is  13.   Multiply  the  latter     (Multiply  by  5)    X  5 

^u-0^/^?'    ,  (fof78)     65 

Multiply  78  by  4  and  \6  ' 

combine  the  two  results.  (4  times  78)  312 

(4f  times  78)  377  Ans. 


A  B  C  D 

a.  84x4f  96x3f  96x4f  84  x  7| 

b.  48x5|  88x6^  85x3f  84  x  8f 

c.  70x4f  96x5J  80  x  6f  84  x  9f 


MIXED  NUMBERS  169 

4.    Multiply  84  by  24f . 


PROCESS 

After  finding  |-  of  84, 

84 

multiply  84  by  4,  plac- 

24f 

ing  the  right-hand  fig- 

(i of  84) 

14 

ure  of  the  product  in 

\  O                         ' 

x5 

•4-T-%A   r\m  ^Q     i**/Vl  n  TTI  n     *f"  n  PTI 

1  I  M      U  1  H   ^>       (   (  H  1  1  1  1  1  1  1  ,     I  1  1  •    1  1 

multiply  84  by  2  tens, 

(1  of  84) 

70 

placing  the  right-hand 

(4  times  84) 

336 

figure  of  the  product  in 

(2  tens  times  84) 

168 

the  tens'  column,  etc. 

(24f  times  84) 

2086  Ans. 

ABC 

a.  36x211      42x33J      48  x  23J- 
I.   75  x  311      84  x  421 
c.  108x15*     112x24f 


d.  180x24f  132xl4f  144x41f 

e.  176x34f  184  x  26*  140x35^ 
/.    140x51f  116x61|  170x52f 
g.   200x62|  150x71|  160x81| 
h.    130xl2|  240x23|  306  x  34* 

Sight  Exercises 
Give  products : 
A  B 

60          60 
xlOf 


c 
40 
xlOf 

D 

50 
xlOf 

E 

50 
xlOf 

F 

50 

170  SECTION   THREE 

Oral  Problems 

1.  "What  is  the  cost  of  a  yard  of  dress  goods  when 
one  half  yard  costs  32  cents  ? 

2.  At  6  pairs  of  stockings  for  a  dollar,  how  many 
pairs  can  be  bought  for  $  4.50  ? 

3.  When  collars  sell  at  2  for  25  cents,  what  is  re- 
ceived for  a  dozen  collars  ? 

4.  How  many  tons  of  hay  are  there  in  two  stacks, 
one  containing  10^  tons  and  the  other  containing  15|- 
tons? 

5.  A  man  has  two  farms  each  containing  64  acres. 
How  many  acres  are  there  in  both  ? 

6.  A  rod  is  16^  feet.     How  many  feet  wide  is  a 
road  that  is  2  rods  wide  ? 

7.  At  60  cents  a  dozen,  how  much  is  paid  for  36 
roses? 

8.  How  many  are  5  J  +  5 \  +  5J  ? 

9.  When  each  house  is  20  feet  wide,  how  many 
houses  can  be  built  on  a  plot  200  feet  wide  ? 

10.  How  many  half-pint  glasses  of  lemonade  are 
there  in  2  gallons  ? 

11.  One  third  of  a  flock  of  sheep  are  in  the  barn. 
How  many  are  there  in  the  flock  if  there  are  32  sheep 
in  the  barn  ? 

12.  How  many  nails  can  be  made  from  a  yard  of 
wire     (a)    when   \  inch   is   needed   for   each   nail  ? 
(6)  When  2  inches  are  needed  ? 


REVIEWS  171 

is.  If  a  pail  of  water  weighs  16  pounds  and  the 
pail  alone  weighs  2J  pounds,  how  many  pounds  does 
the  water  weigh  ? 

14.  If  \  peck  of  wheat  weighs  7 \  pounds,  what  is 
the  weight  (a)  of  a  peck  ?  (6)  Of  2  pecks  ?  (c)  Of  4 
pecks  ? 

is.  A  freight  car  can  carry  100  thousand  pounds. 
How  many  tons  of  2  thousand  pounds  each  can  it 
carry? 

16.  A  steel  freight  car  weighs  22  tons  of  2  thousand 
pounds  each.    How  many  pounds  does  it  weigh  ? 

17.  Taking  1  pound  as  the  weight  of  a  pint  of  water, 
what  is  the  weight  of  a  3-gallon  pail  of  water,  when 
the  pail  weighs  6  pounds  ? 

is.  At  25  cents  a  pound,  how  many  pounds  of 
coffee  can  be  purchased  (a)  for  $  1  ?  (5)  For  $2  ? 
(c)  For  $4? 

19.  If  a  gallon  of  paint  will  cover  300  square  feet, 
how  many  gallons  are  needed  to  paint  1,800  square 
feet? 

20.  At  the  rate  of  3  pounds  of  flour  to  4  pounds  of 
bread,  how  many  pounds  of  bread  will  30  pounds  of 
flour  make  ? 

21.  If  the  dough  weighs  |-  more  than  the  flour, 
how  many  pounds  of  dough  will  20  pounds  of  flour 
make? 

22.  The  sum  of  2  numbers  is  60 ;  one  of  the  num- 
bers is  26.     What  is  the  other? 


172  SECTION  THREE 

Written  Problems 

1.  What  is  the  cost  of  a  yard  of  cloth  when  one 
eighth  of  a  yard  costs  22  cents  ? 

2.  At  3  pairs  of  stockings  for  50  cents,  how  many 
pairs  can  be  bought  for  $  3.50  ? 

3.  When  cuffs  sell  at  2  pairs  for  45  cents,  what  is 
received  for  a  dozen  pairs  ? 

4.  How  many  tons  of  hay  are  there  in  3  stacks, 
containing,  respectively,  10J  tons,  12^  tons,  and  14^- 
tons? 

s.   A  farm  consists  of  3  fields  each  containing  36|- 
acres.     How  many  acres  are  there  in  the  farm  ? 

6.  How  many  feet  wide  is  a  road  4  rods  wide,  a 
rod  being  3  yards  of  5^  feet  each  ? 

7.  At  $  1  per  dozen,  how  much  is  paid  for  66 
roses  ? 

s.    How  many  are  IGI+IGJ+IGJ  +  IGJ+IGJ? 

9.   When  each  house  is  25  feet  wide,  how  many 
houses  can  be  built  on  a  plot  600  feet  wide  ? 

10.  How  many  half-pint  glasses  of  lemonade  are 
there  in  5  gallons  ? 

11.  One  sixth  of  a  flock  of  sheep  are  in  the  barn. 
How  many  sheep  are  there  in  the  flock  if  there  are 
35  in  the  barn. 

12.  How  many  nails  can  be  made  from  5  yards  of 
wire  if  ^  inch  is  used  in  making  each  nail  ? 


WRITTEN   REVIEW  173 

13.  If  a  barrel  with  the  flour  weighs  220^  pounds 
and  the  barrel  weighs  24^-  pounds,  how  many  pounds 
of  flour  does  it  contain  ? 

14.  When  J  peck  of  potatoes  weighs  3J  pounds, 
find  the  weight  of  the  potatoes  in  a  barrel  contain- 
ing 2^-  bushels. 

is.    How  many  tons  of   2,240  pounds  each  make 
98,560  pounds? 

16.  How  many  pounds  less  than  44,000  does  a  car 
weigh  that  weighs  19  tons  of  2,240  pounds  each  ? 

17.  Assuming  that  a  pint  of  water  weighs  a  pound, 
what  is  the  weight  of  a  40-quart  can  filled  with  water 
when  the  can  weighs  25  pounds  ? 

is.    My  bill  for  coffee  at  25  cents  per  pound  was 
$  11.25.     How  many  pounds  did  I  buy? 

19.  If  a  gallon  of  paint  will  cover  315  square  feet, 
how  many  gallons  will  be  needed   to  paint  a  fence 
containing  1,890  square  feet? 

20.  At  the  rate  of  3  pounds  of  flour  to  4  pounds  of 
bread,  how  many  pounds  of  bread  will  195  pounds  of 
flour  make  ? 

21.  If  the  dough  weighs  1|-  times  as  much  as  the 
flour,  how  many  pounds  of  dough  will  195  pounds  of 
flour  make  ? 

22.  The  sum  of  two  numbers  is  117.     One  of  the 
numbers  is  79.     Find  the  other  number. 

23.  What  number  multiplied  by  32  gives  a  product 
of  480  ? 


174  SECTION  THREE 

Denominate  Numbers 

Long  Measure 

12  inches  (in.)     1  foot  (ft.) 
3  feet  1  yard  (yd.) 

5^  yards  1  rod  (rd.) 

320  rods  1  mile  (mi.) 

Oral  Problems 

1.  How  many  houses,  each  20  feet  wide,  can  be 
built  from  First  Street  to  Second  Street  if  the  build- 
ing space  is  200  feet  ? 

2.  "What  is  the  distance  from  the  middle  of  First 
Street  to  the  middle  of  Second  Street  if  each  street  is 
50  feet  wide,  the  sidewalk  on  each  street  is  7  feet 
wide,  and  the  building  space  is  200  feet  ? 

3.  How  many  houses,  each  20  feet  wide,  can  be 
built  from  Avenue  A  to  Avenue  B  if  the  building 
space  is  800  feet  ? 

4.  What  is  the  distance  from  the  middle  of  Avenue 
A  to  the  middle  of  Avenue  B  if  each  avenue  is  60 
feet  wide,  the  sidewalk  on  each  avenue  is  10  feet  wide, 
and  the  building  space  is  800  feet  ? 

5.  What  part  of  a  mile  is  the  length  of  a  square 
field,  if  each  side  measures  80  rods  ? 

6.  How  many  feet  are  there  in  a  rod  ? 

7.  If  there  are  20  streets  to  a  mile,  how  far  do  you 
walk  in  going  from  60th  Street  to  85th  Street  ? 


DENOMINATE  NUMBERS  175 

Written  Problems 

1.  Fill  the  blanks  in  the  following : 

1  mi.  =  320  rd.  =  —  yd.  =  —  ft. 
1  rd.  =  5lyd.  =  — ft. 

2.  When  a  man's  pace  measures  3  feet,  how  many 
paces  are  there  in  J  mile  ? 

3.  If  a  boy's  pace  is  2^  feet,  how  many  yards  are 
equal  to  120  paces  ? 

4.  When  railroad  ties  are  3  feet  apart,  how  many 
ties  are  there  to  a  mile  ? 

5.  How  many  dollars  will  pay  for  1,320  railroad 
ties  at  $  \  each  ? 

6.  How  many  rails  each  60  feet  long  will  make  a 
mile? 

7.  At  18  pounds  to  the  yard,  find  the  weight  of 
one  60-foot  rail. 

8.  Measure  the  length  of  a  page  of  your  book. 
Measure  the  length  of  the  cover.     Find  the  difference 
between  the  two  lengths. 

9.  When  streets  are  264  feet  apart  how  many 
streets  are  there  to  a  mile  ? 

10.  When  avenues  are  880  feet  apart,  how  many 
avenues  are  there  to  a  mile  ? 

11.  How  many  miles  does  a  person  walk  in  going 
from  Avenue  A  to  Avenue  I  and  from  18th  Street  to 
33d  Street  ? 


176  SECTION  THREE 

Areas 
Oral  Exercises 

1.  (a)    How  many  square   inches  are  there  in  a 
square  2  inches  long?     (6)    In  a  rectangle  2  inches 
long,  ^  inch  wide  ?     (c)    In  a  rectangle  2^  inches  long, 
2  inches  wide  ? 

2.  How  many  square  feet  in  a  blackboard  8^  feet 
long,  4  feet  wide  ? 

3.  How  many  square  feet  in  a  door  6  feet  high,  2^ 
feet  wide  ? 

4.  How  many  square  feet  in  two  windows  each  5 
feet  high,  2-J  feet  wide  ? 

5.  How  many  square   yards  in  a  floor   6  yards 
long,  4^  yards  wide  ? 

6.  How  many  square  yards  in  a  piece  of  carpet  36 
yards  long,  f  yard  wide  ? 

7.  How  many  square  inches  in  a  square  12  inches 
long,  12   inches   wide?     In  a  square    1   foot   long, 
1  foot  wide? 

8.  How  many  square  feet  in  a  city  lot  (a)  20  feet 
by  100  feet?     (6)  25  feet  by  100  feet?     (c)  30  feet 
by  150  feet? 

9.  How  many  square  feet  are  there  (a)  in  4  city 
lots,  each  measuring  20  feet  by  100  feet  ?     (6)  In  40  ? 

10.  There  are  160  square  rods  in  an  acre,  (a)  How 
many  square  rods  in  10  acres  ?  (&)  How  many  acres 
in  a  square  field  40  rods  long  ? 


AREAS  177 

Written  Exercises 
Square  Measure 

144  square  inches  (sq.  in.)     1  square  foot  (sq.  ft.) 
9  square  feet  1  square  yard  (sq.  yd.) 

NOTE.  To  find  the  area  in  square  inches,  express  each  dimen- 
sion in  inches;  to  find  the  area  in  square  feet,  express  each 
dimension  in  feet ;  to  find  the  area  in  square  yards  express  each 
dimension  in  yards. 

1.  Find  the  area  of  a  rug  54  inches  wide,  72  inches 

long. 

The  number  of  square  inches  =  54  X  72. 
The  number  of  square  feet  =  4^  x  6. 
The  number  of  square  yards  =  \\  x  2. 

2.  Find  the  number  of  square  inches  in  each  of  the 
following  rectangles : 

a.  Length,  48  inches ;  width,  42  inches. 

b.  Length,  4  feet ;  width,  42  inches. 

c.  Length,  4  feet;  width,  3^  feet. 

3.  Find  the  number  of  square  feet  in  each  of  the 
following  rectangles: 

a.  Length,  4  feet ;  width,  3^-  feet. 

b.  Length,  54  feet ;  width,  60  inches. 

c.  Length,  120  feet;  width,  25  feet. 

4.  Find  the  number  of  square  yards  in  each  of  the 
following  rectangles : 

a.  Length,  36  yards ;  width,  f  yard. 

b.  Length,  108  feet;  width,  27  inches. 

c.  Length,  48  yards  ;  width,  37J  yards. 


178  SECTION  THREE 

Measurements 
Written  Problems 

1.  A  room  is  18  feet  long,  12  feet  wide,  9  feet  high. 

a.  Find  the  number  of  square  feet  in  the  floor. 

b.  How  many  square  yards  of  carpet  will  cover 
the  floor? 

c.  Find  the  number  of  square  feet  in  the  ceiling. 

d.  How  many  running  feet  of  baseboard  are  there 
in  four  sides  of  the  room,  deducting  3  feet  for  the 
space  taken  by  a  door? 

e.  How  many  square  feet  of  baseboard  are  there 
in  the  room,  when  the  baseboard  is  one  foot  high  ? 

2.  A  paper  cracker  box  is  8  inches  long,  3  inches 
wide,  3  inches  high. 

a.  How  many  square  inches  of  paper  are  required 
for  each  of  the  square  ends  ? 

6.  How  many  square  inches  of  paper  are  required 
for  each  of  the  four  long  faces  ? 

c.  How  many  square  inches  of  paper  are  required 
for  all  six  faces,  making  no  allowance  for  overlapping  ? 

d.  How  many  crackers  3  inches  square  will  it  hold, 
if  each  cracker  is  J-  inch  thick  ? 

3.  How  many  square  feet  of  wall  paper  are  there  in 
a  roll  of  paper  18  yards  long,  18  inches  wide? 

4.  At  $  1.50  per  square  yard,  what  will  be  the  cost 
of  the  linoleum  covering  a  kitchen  15  feet  square  ? 

s.  A  fence  on  the  front  of  a  lot  is  25  feet  long  and 
6  feet  high.  How  many  square  feet  does  it  contain  ? 


VOLUMES  179 

Cubical  Contents 
Preparatory  Exercises 

1.  (a)  How  many  one-inch 
cubes   can  be   placed  on  the 
bottom    of    a    box    5   inches 
long,  4  inches  wide?     (6)  If 
the    box    holds    3    layers   of 
one-inch    cubes,    how    many 
one-inch  cubes  will  the  box  hold  ? 

2.  A  box  6  inches  long,  5^  inches  wide,  and  7 
inches  high  will  hold  exactly  a  gallon.     How  many 
cubic  inches  are  there  in  a  gallon  ? 

3.  How  many  one-inch   cubes  can  be  put  into  a 
cracker  box  3  inches  by  3  inches  by  8  inches  ? 

4.  Carefully  balance  an  empty  pint  measure  by 
placing  sand  on  the  opposite  pan  of  the  scales,  then 
fill  the  measure  with  water  and  ascertain  the  weight 
of  the  water. 

s.  (a)  Find  the  number  of  cubic  inches  in  a  cube  12 
inches  long,  12  inches  wide,  12  inches  high.  (6)  How 
many  cubic  feet  does  it  contain?  (c)  How  many 
cubic  inches  are  there  in  a  cubic  foot? 

6.  (a)  How  many  cubic  feet  are  there  in  a  cube  3 
feet  long,  3  feet  wide,  3  feet  high  ?     (6)  How  many 
cubic  feet  are  there  in  a  cubic  yard  ? 

7.  Give  the  capacity  of  a  bin  measuring,  on  the 
inside,  2  yards  long,  2  yards  wide,  2  yards  high. 


180  SECTION  THREE 

Volumes 


To  find  the  volume  of  a  solid  means  to  find  the 
number  of  cubic  inches,  cubic  feet,  cubic  yards,  etc., 
it  contains. 


A  solid  having  six  rectangular  faces  is  called  a 
rectangular  prism.  The  opposite  faces  of  a  rectangu- 
lar prism  are  equal  in  area.  When  each  of  the  six 
faces  is  a  square,  the  solid  is  called  a  cube. 

A  caramel  is  a  rectangular  prism,  so  is  a  brick, 
a  box,  a  room,  etc. 

A  rectangular  prism  has  three  dimensions ;  length, 
width,  and  thickness. 


To  find  the  number  of  cubic  inches,  cubic  feet,  cubic 
yards,  etc.,  in  a  rectangular  prism,  multiply  the  number 
of  inches,  feet,  yards,  etc.,  in  its  length,  by  the  number 
of  the  same  denomination  in  its  width,  and  this  product 
by  the  number  of  the  same  denomination  in  its  thickness. 


Table 

Cubic  Measure 

1728  cubic  inches  (cu.  in.)     1  cubic  foot  (cu.  ft.). 
27  cubic  feet  1  cubic  yard  (cu.  yd.). 


1  cubic  foot  =  7J  gallons  (nearly). 
1  cubic  foot=    J  bushel  (nearly). 


RECTANGULAR  PRISMS 


181 


Written  Exercises 

1.  How    many    cubic 
feet  are  there  in  a  pile  of 
wood  8  feet  long,  4  feet 
wide,  4  feet  high  ? 

NOTE.     A  pile  of  wood  8  ft.  by  4  ft.  by  4  ft.  contains  a  cord. 

2.  How  many  cubic  feet  of  grain  can  be  placed  in 
a  bin  5  feet  long,  5  feet  wide,  5  feet  high  ? 

3.  At  ^  bushel  to  the  cubic  foot,  how  many  bushels 
are  there  in  125  cubic  feet  ? 

4.  A  cubic  foot  of   water  weighs  1,000  ounces. 
How  many  pounds  does  it  weigh  ? 

5.  At  62|-  pounds  to  the  cubic  foot,  what  is  the 
weight  of  128  cubic  feet  of  water  ? 

6.  At  31 J  pounds  to  the  cubic  foot,  what  is  the 
weight  of  a  cord  of  wood  (128  cu.  ft.)  ? 

7.  If  a  cart  body  is  4  feet  long  and  3  feet  wide, 
how  high  must  it  be  to  hold  27  cubic  feet  ? 

8.  When  dry  sand  weighs  86  pounds  to  the  cubic 
foot,  what  is  the  weight  of  a  cart  load  containing  22 
cubic  feet  ? 

9.  How  many  cubic  feet  are  there  in  a  wagon  body 
6  feet  long,  4 \  feet  wide,  1  \  feet  high  ? 

10.   What  is  the  weight  of  a  cubic  yard  of  sand 
weighing  86  pounds  to  the  cubic  foot  ? 


182  SECTION  THREE 

11.  How  many  cubic  yards  are  there  in  a  box  2 
yards  long,  1^-  yards  wide,  \  yard  high  ? 

12.  How  many  cubic  feet  are  there  in   1^   cubic 
yards  ? 

13.  At  7^  gallons  to  a  cubic  foot,  how  many  gallons 
of  water  will  fill  a  tank  8  feet  long,  4  feet  wide,  4 
feet  high  ? 

14.  How  many  cubic  feet  of  earth  are  removed 
in  digging  a  cellar  50  feet  long,  20  feet  wide,  and 
9  feet  deep  ? 

is.  How  many  cubic  yards  of  air  are  there  in  a 
room  18  feet  long,  12  feet  wide,  and  9  feet  high  ? 

16.  (a)  How  many  cubic  feet  are  there  in  a  timber 
16  feet  long,  6  inches  wide,  3  inches  thick  ?  (6)  what 
is  its  weight  at  40  pounds  to  the  cubic  foot  ? 


SECTION   IV 

REVIEW  AND  SUPPLEMENTARY  WORK 
Notation  and  Numeration 

For  convenience  in  reading  large  numbers  divide 
them  by  commas  into  periods  of  three  figures  each, 
beginning  at  the  right. 

TABLE 


WHO  WHO  WHO 

123,          456,          789 

Millions'  Thousands'  Ones' 

Period  Period  Period 

In  reading  numbers  omit  the  name  of  the  ones' 
period.  Read  789,  seven  hundred  eighty-nine. 

Read  6,789,   6  thousand  789. 

Read  3,456,789,  3  million  456  thousand  789. 

The  periods  above  the  third  are  named  billions1 
period,  trillions'  period,  etc. 

Omit  the  name  of  a  period  consisting  exclusively 
of  ciphers.  Thus,  read  14,000,000  as  14  million ; 
6,000,375  as  6  million  375. 

Do  not  use  a  comma  in  writing  a  number  of  four 
figures  denoting  a  year. 

Numbers  of  four  figures  are  frequently  read  as  hun- 
dreds ;  as,  19  hundred  10.  The  word  hundred  is  also 
omitted ;  as,  nineteen  ten. 

183 


184  SECTION   FOUR 

Oral  Exercises 
Read  the  following : 


a. 
6. 
c. 
d. 

e. 

A 

250,000 
173,086 
45,297 
6,050 
23,915 

B 

1,205,060 
789,516 
2,314,800 
6,519,260 
800,000 

C 

23,004,005 
3,000,486 
28,000,000 
36,050,000 
5,060,000 

D 

103,206,580 
215,387,614 
319,600,000 
48,600,000 
562,009,007 

/   456,808     3,465,292     45,103,950     643,870,530 

Written  Exercises 
Express  in  figures : 

1.  Three  hundred  seventy-two  thousand. 

2.  One  million,  forty-two  thousand,  six  hundred. 

3.  Ten  million,  fifty  thousand,  seventy. 

4.  One  hundred  seventy-five  million,  two  hundred 
three  thousand,  six  hundred. 

5.  Eighty -four  million,  seven  hundred  twenty-two 
thousand,  three  hundred  ninety-five. 

6.  Two  million,  five  thousand,  three. 

7.  One  hundred  six  million,  three  hundred  ten 
thousand,  eight. 

8.  Nine  hundred  eighty-seven  million,  six  hundred 
fifty-four  thousand,  three  hundred  twenty-one. 

9.  Five  hundred  million,  two  thousand,  one. 

10.    Seven  hundred  eighty-five  million,  two  hundred 
forty-four  thousand,  nine  hundred  fifty-six. 


REVIEWS  185 

Addition  and  Subtraction 
Sight  Drills 

1.  Add  128  to  each  of  the  following  numbers  : 

ABCDEFGH          I        J 

a.  93  26  92  66  84  74  96  15  87  78 

b.  64  57  36  44  38  53  28  67  91  86 

c.  46  34  83  25  77  88  56  85  76  37 

d.  82  18  65  14  45  95  73  27  14  55 

e.  25  73  47  58  98  17  35  68  94  48 

2.  Subtract  each  of  the  foregoing  numbers  from 
210. 

3.  Add  350  to  each  of  the  following  numbers: 


A 

B 

c 

D 

E 

F 

a. 

190 

125 

56 

1,050 

2,700 

155 

b. 

270 

216 

67 

2,060 

3,800 

256 

c. 

350 

137 

78 

3,070 

4,900 

357 

d. 

480 

325 

89 

4,080 

5,800 

458 

e. 

560 

445 

95 

5,090 

6,700 

559 

4.    Give  answers  rapidly  : 

Think  221  +  100  +  50+6.     Think  221  -  100  -  50  -  6. 


A 

B 

c 

a. 

221  +  156 

422-363 

362  +  284 

b. 

221-156 

540  +  451 

362-284 

c. 

334  +  245 

540-451 

273  +  175 

d. 

334-245 

431  +  362 

273-175 

e. 

422  +  363 

431-362 

184  +  122 

186  SECTION  FOUR 


Addition  and  Subtraction 

Written  Exercises 

1. 

Find  sums.     Test  : 

A 

B 

C 

a. 

612,345 

2,543,876 

37,873,887 

89,764 

264,668 

6,525,307 

7,652 

4,828,748 

895,400 

98,030 

402,606 

67,859 

204,786 

90,090 

242,784 

88,359 

825,163 

68,135 

\ 

f          P  ^KvVS^ 

I. 

842,735 

7,369,644 

78,642,371 

94,681 

377,180 

1,945,852 

27,658 

92,143 

647,481 

248,569 

869,515 

25,635 

60,370 

4,625,790 

847,162 

85,396 

608,405 

3,836,505 

c. 

714,653 

6,833,726 

2,439,876 

94,728 

188,706 

60,400 

615,840 

548,057 

294,501 

53,174 

64,382 

804,975 

58,034 

1,008,590 

2,800,463 

65,348 

438,249 

858,674 

2.   Find  differences  without  rearranging : 

-83,604  -890,089  45,305,902 

600,000  1,234,567  -7,408,904 


REVIEWS  187 


3.   Add: 

• 

A 

B 

c 

a.    $123,456.78 

$   94,309.82 

$767,088.00 

90,312.20 

172,074.55 

126,435.79 

6,734.87 

99,873.00 

205,719.65 

539,314.60 

67,021.45 

80,482.36 

619,512.14 

216,835.50 

198,060.00 

6.    $854,923.74 

$270,050.66 

$820,932.32 

45,024.58 

382,104.20 

88,150.08 

7,056.00 

92,307.55 

26,934.45 

304,729.68 

81,256.43 

342,345.00 

51,120.09 

507,759.00 

6,437.46 

c.    $  -82,559.24 

$895,694.63 

$450,880.77 

76,385.64 

96,438.00 

57,028.24 

371,626.00 

42,740.08 

96,462.50 

27,842.96 

138,128.72 

792,664.82 

381,730.53 

69,569.06 

48,125.82 

78,473.75 

70,591.76 

38,484.57 

4.   Insert  missing  addend  : 

A 

B 

C 

a.        $  157,943.87 

? 

$345,678.90 

-1-           ? 

+  $983,654.63 

f           ? 

$  200,000.00 

$1,000,000.00 

$  1,234,567.89 

6.        $   82,559.24 

$895,694.63 

? 

76,385.64 

? 

$    350,880.77 

? 

96,438.00 

792,664.23 

$  200,000.00 

$1,000,000.00 

$  1,234,567.89 

188  SECTION  FOUR 

Multiplication  and  Division 

Drill  Exercises 
1.    Give  products: 

Say  twice  two  ten  are  four  twenty,  four  times  six  ten  are 
twenty-four  forty.     Omit  the  words  hundred  and  thousand. 


A 

B 

C 

D 

a. 

2 

X 

210 

3 

x210 

4x 

210 

5 

X 

210 

6. 

2 

X 

310 

3 

X 

310 

4x 

310 

5 

X 

310 

c. 

2 

X 

410 

3 

X 

410 

4x 

410 

5 

X 

410 

d. 

2 

X 

510 

3 

X 

510 

4x 

510 

5 

X 

510 

e. 

2 

X 

610 

3 

X 

610 

4x 

610 

5 

X 

610 

E 

F 

G 

H 

a. 

6 

X 

210 

7 

X 

210 

8x 

210 

9 

X 

210 

b. 

6 

X 

310 

7 

X 

310 

8x 

310 

9 

X 

310 

c. 

6 

X 

410 

7 

X 

410 

8x 

410 

9 

X 

410 

d. 

6 

X 

510 

7 

X 

510 

8x 

510 

9 

X 

510 

e. 

6 

X 

610 

7 

X 

610 

8x 

610 

9 

X 

610 

2.    Give  quotients  and  remainder,  if  any  : 

Think  two  ten  into  fourteen  seventy,  etc. 

A  B  C  D 

a.   210)1,470     210)1,890     210)1,260  210)1,680 

6.   310)1,550     310)2,480     310)1,860  310)2,180 

c.  410)3,700     410)1,640     410)2,500  410)2,050 

d.  510)2,040     510)3,670     510)1,540  510)4,600 

e.  610)5,500     610)1,830     610)3,070  610)4,880 
/    710)5,000     710)1,430     710)6,400  710)5,680 


REVIEWS  189 

Oral  Problems 

1.  A  man  went  from  New  York  to  Baltimore,  184 
miles,  and  then  from  Baltimore  to  Washington,  40 
miles.     How  far  did  he  travel  from  New  York  to 
Washington  ? 

2.  At  32  miles  per  hour  how  long  would  it  take 
a  train  to  go  960  miles  ? 

3.  What  is  the  weight  of  40  bushels  of  oats  at 
32  pounds  to  the  bushel  ? 

4.  Twelve  hundred  eighty  pounds  are  how  many 
pounds  less  than  twenty  hundred  pounds  ? 

5.  At  320  rods  to  the  mile,  how  many  rods  are 
there  in  4  miles  ? 

6.  How  many  working  days  are  there  in  a  year 
of  365  days,  excluding  52  Sundays  and  4  holidays? 

7.  How  many  J-acre  plots  are  there  in  a  piece  of 
ground  containing  16  acres? 

8.  If  a  man  walks  1\  miles  to  his  work  and  2J 
miles  back,  how  many  miles  does  he  walk  in  a  year 
of  309  working  days  in  going  to  work  and  returning? 

9.  How  many  square  feet  are  there  in  a  tight 
fence  6  feet  high  around  a  square  plot,  each  side 
measuring  200  feet  ? 

10.  Find  how  much   less  than  $  100  will  be  the 
cost  of  80  hammocks  at  $  1.10  each. 

11.  How  much  change  is  given  when  a  $  20  bill  is 
given  for  a  purchase  of  $  18.40  ? 


190  SECTION  FOUR 

Multiplication 
Written  Exercises 
Multiply.     Test : 


A 

B 

c 

a. 

415 

X 

306 

1,205 

X 

308 

1,504 

X 

1,307 

b. 

421 

X 

509 

1,307 

X 

345 

1,498 

X 

1,406 

c. 

123 

X 

876 

1,406 

X 

403 

1,234 

X 

4,301 

d. 

234 

X 

543 

1,508 

X 

512 

1,407 

X 

2,048 

e. 

316 

X 

435 

2,042 

X 

332 

2,305 

X 

1,352 

/• 

423 

X 

316 

2,105 

X 

623 

1,234 

X 

1,234 

9- 

538 

X 

243 

3,016 

X 

712 

1,357 

X 

2,468 

h. 

641 

X 

165 

4,204 

X 

805 

1,536 

X 

1,243 

i. 

812 

X 

143 

1,234 

X 

916 

2,135 

X 

1,354 

j- 

924 

X 

122 

1,345 

X 

821 

3,216 

X 

1,234 

L 

844 

X 

137 

2,123 

X 

777 

2,123 

X 

2,331 

I 

763 

X 

204 

3,214 

X 

666 

3,214 

X 

1,332 

m. 

627 

X 

212 

4,125 

X 

555 

4,125 

X 

1,665 

n. 

586 

X 

423 

1,326 

X 

987 

1,263 

X 

4,164 

o. 

437 

X 

514 

2,314 

X 

876 

2,143 

X 

2,468 

P- 

359 

X 

625 

3,245 

X 

765 

3,425 

X 

1,357 

<!• 

286 

X 

713 

4,216 

X 

654 

4,162 

X 

2,579 

r. 

175 

X 

826 

5,135 

X 

543 

5,531 

X 

3,467 

s. 

298 

X 

735 

4,424 

X 

432 

4,244 

X 

4,253 

t. 

367 

X 

642 

3,571 

X 

321 

3,157 

X 

3,275 

u. 

406 

X 

457 

2,809 

X 

246 

4,356 

X 

2,345 

v. 

584 

X 

318 

1,763 

X 

357 

2,824 

X 

3,609 

REVIEWS  191 

Long  Division 
Written  Exercises 

1.  Divide.     Test: 

\          A  B  C  D 

«>9,177-19  9,432-*- 18  9,129-^-17  9,120-5-16 

b.  9,773-29  9,660-*- 28  9,828-27  9,386-26 

c.  9,555-39  8,968-38  9,250-37  9,252-36 

d.  9,163-5-49  8,400-48  9,071  -i-  47  9,062-46 

e.  9,617-59  9,106-5-58  9,519-57  9,576-56 
/  8,832-69  9,044-68  9,916-67  9,900-66 
g.  5,925-79  5,148-78  9,625-77  9,652-76 
h.  7,298-89  6,864-5-88  7,569-87  7,568-86 

i.    6,237-99     8,134-98      9,894-5-97     9,984-96 

\ 

2.  Divide.     Test : 

A  B  C 

a.  8,159-199        61,854-793         608,006-5-634 

b.  9,536-298         47,276-892         472,515-545 

c.  9,131-5-397         33,694-991         336,528-456 

d.  7,936-496         58,565-901         585,365-5-367 

3.  Divide.     Test: 

A  B 

a.   974,036-5-1,204  1,522,756-5-1,234 

6.  827,431-5-2,033  4,704,070-2,345 

c.  925,344-3,024  9,381,372-5-3,124 

d.  953,428-4,006  8,417,040-5-4,126 

e.  903,060-1-5,017  5,548,040-5-5,234 


192  SECTION  FOUR 

Oral  Problems 

1.  A  gross  is  12  dozen.    How  many  pencils  (a)  in 
\  gross  ?     (&)  In  \  gross  ?     (c)  In  J  gross  ?     (d)  In 
J  gross  ? 

2.  How  many  quarts  of  oil  are  there  in  a  barrel 
containing  51  gallons  ? 

3.  From  a  farm  of  300  acres,  261  acres  were  sold. 
How  many  acres  were  not  sold  ? 

4.  How  many  quarter-dollars  are  there  in  $  22  ? 

5.  Mr.  Alphin  sets  out  88  hundred  cabbage  plants 
in  44  rows.    How  many  plants  are  there  in  each  row  ? 

6.  If  a  wagon  weighs  12  hundred  pounds  and  the 
straw  on  it  weighs  22  hundred  pounds,  what  is  the 
weight  of  both  ? 

7.  From  a  barrel  of  oil  containing  50  gallons  10 \ 
gallons  were  sold.     How  many  gallons  remain  ? 

8.  How  many  days  (a)  in  50  weeks  ?     (6)  In  2 
weeks  ?     (c)  In  52  weeks  ? 

9.  How  many  dollars  are  there  in  888  quarter 
dollars  ? 

10.  How  many  days  will  48  pounds  of  butter  last 
if  16  pounds  are  used  in  a  week  ? 

11.  If  a  man  earns  $  125  per  month  and  his  ex- 
penses are  $  94  per  month,  how  many  dollars  can  be 
saved  (a)  in  a  month  ?     (6)  In  a  year  ? 

12.  What  is  the  weight  of  1,000  common  bricks  at 
I    Ib.  each  ? 


REVIEWS  193 

13.  At  160  bricks  per  day,  how  many  days  are  re- 
quired to  lay  960  bricks  ? 

14.  What  is  the  cost  of  a  cement  walk  3  feet  wide, 
100  feet  long,  at  8  cents  per  square  foot? 

is.  A  man  takes  an  automobile  trip  40  miles  and 
back  at  the  rate  of  8  miles  per  hour  going,  and  10 
miles  per  hour  returning.  How  long  does  he  require 
for  the  trip  ? 

is.  I  bought  20  yards  of  velvet  for  $  70  and  sold 
it  at  a  profit  of  $  J  per  yard.  How  much  per  yard 
did  I  receive  for  it  ? 

17.  Two  boys  start  from  the  same  point  and  travel 
in  opposite  directions  at  the  rate  of  2J-  miles  per  hour. 
How  far  apart  are  they  in  5  hours  ? 

is.  What  is  the  cost  of  a  horse  and  a  wagon  if  the 
horse  cost  $250  and  the  wagon  cost  $125  ? 

19.  A  field  is  300  yards  square.     How  many  yards 
of  wire  will  be  required  to  inclose  it  with  a  fence  4 
wires  high  ? 

20.  A  man  bought  a  lot  for  $650,  giving  12  cows, 
for  which  he  was  allowed  $50  each,  and  the  balance 
in  cash.     How  much  cash  did  he  give  ? 

21.  After  selling  one   half  of  his  crop  of  cotton 
Judge  Wilson  has  324  bales  left.     Of  how  many  bales 
did  the  crop  consist  ? 

22.  A  boy  used  224  of  a  bunch  of  250  shingles  in 
mending  a  roof.      How  many  shingles  were  left  ? 


194  SECTION  FOUR 

Written  Problems 

1.  A  great  gross  consists  of  12  gross  of  12  dozen 
each.     How  many  pens  are  there  in  one  half  of   a 
great  gross  ? 

2.  How  many  quarts  of  oil  are  there  in  49  gallons  ? 

3.  From  a  farm   of   300    acres  137J  acres  were 
sold.     How  many  acres  remain  ? 

4.  How  many  quarter  dollars  are  there  in  $  27J  ? 

5.  If   9,180  cabbage  plants  are  required    for  45 
rows,  how  many  plants  are  there  to  a  row  ? 

6.  A  wagon  weighs  1,245  Ib.  and  the  straw  on 
it  weighs  2,156  Ib.     What  is  the  weight  of  both  ? 

7.  From  a  barrel   of   oil  containing  50    gallons, 
three  lots  were  sold  of  10J  gallons  each.     How  many 
gallons  remain  ? 

8.  How  many  days  are  there  in  26  weeks  ? 

9.  How  many  dollars   are   there  in  972  quarter 
dollars  ? 

10.  How  many  days  will  255  pounds  of  butter  last 
if  17  pounds  are  used  each  week  ? 

11.  If  a  man  earns  $  112.50  per  month  and  his  ex- 
penses are  $  83.75  per  month,  how  many  dollars  can 
he  save  in  (a)  1  month  ?  (&)  1  year  ?  (c)  2  years  ? 

12.  A  girl  makes  a  steamboat  trip  of  100  miles  and 
back  at  the  rate  of  16  miles  per  hour  going  and  12 
miles  per  hour  returning.     How  many  hours  are  re- 
quired for  the  round  trip  ? 


REVIEWS  195 

is.  What  is  the  weight  of  960  common  bricks  at 
1^  pounds  each  ? 

14.  At  160  bricks  per  day,  how  many  days  are  re- 
quired to  lay  4,000  bricks  ? 

is.  At  10  cents  per  square  foot,  what  is  the  cost 
of  a  cement  walk  5  feet  wide,  164  feet  long  ? 

16.  A  dealer  bought  32  yards  of  cloth  for  $  80  and 
sold  it  at  a  profit  of  $  J  per  yard.     How  much  did  he 
receive  for  it  per  yard  ? 

17.  Two  boys  start  from  the  same  point  and  travel 
in  opposite  directions,  each  going  at  the  rate  of  2j- 
miles  per  hour.     How  far  apart  are  they  in  8  hours  ? 

is.  What  is  the  cost  of  a  horse,  a  wagon,  and  a  set 
of  harness,  if  the  horse  cost  $  375,  the  wagon  $  150, 
and  the  harness  $35  ? 

19.  A  field  is  256  yards  square.     How  many,  yards 
of  wire  will  inclose  it  with  a  fence  4  wires  high? 

20.  A  man  bought  a  lot  for  $800,  giving  12  cows 
at  the  rate  of  $55  each  and  the  remainder  in  cash. 
How  much  cash  did  he  give  ? 

21.  After  selling  three  fourths  of  his  crop  of  hay 
Mr.  Whitlock  has  123  tons  left.      How  many  tons 
were  there  in  the  crop  ? 

22.  A  boy  uses  787  shingles  out  of  4  bunches  of 
250  shingles  each.     How  many  shingles  are  left? 

23.  How  many  tons  of  2,240  pounds  each  do  1,600 
paving  bricks  weigh  if  a  brick  weighs  7  pounds  ? 


196  SECTION  FOUR 

Aliquot  Parts  of  Dollar 
Oral  Exercises 

1.  How  many  dollars  are  equal  to  44  half  dollars  ? 

2.  What  is  the  cost  of  2  dozen  baseballs  at  $^ 
each? 

3.  How  much  must  be  paid  for  48  yards  of  dress 
goods  at  50  cents  per  yard  ? 

4.  A  girl  has  saved  12  dollars  and  12  half  dollars. 
How  much  has  she  saved  ? 

5.  Find  the  cost  of  2  dozen  straw  hats   at  $1J 
each. 

6.  A  man  cut  down  64  trees,  each  yielding  1^  cords 
of  wood.     How  many  cords  of  wood  did  he  cut  ? 

7.  What  will  be  received  for  cutting  64  cords  of 
wood  at  $1^  per  cord? 

8.  -At  25  cents  per  dozen,  what  is  received  for  48 
dozen  eggs  ? 

9.  What  is  the  yearly  cost  of  a  newspaper  at  25 
cents  per  month  ? 

10.  At  25  cents  each,  what  is  the  cost  of  88  readers  ? 

11.  When  meat  is  25  cents  per  pound,  how  much 
does  the  butcher  receive  for  168  pounds? 

12.  If   4  pairs  of   cuffs  cost  a  dollar,  how  many 
pairs  can  be  bought  for  $  42  ? 

is.  At  4  for  a  dollar,  how  many  baseballs  can  be 
bought  for  $  12  ? 

14.    How  many  50-cent  baseballs  will  cost  $  24  ? 


REVIEWS  197 

Sight  Exercises 
i.    Give  the  cost  of  each  of  the  following  items : 

a.    120  yards  of  silk  @  $  1.50  per  yard. 

$120  + 1  of  $120. 
6.    248  gallons  of  sirup  @  50  cents  per  gallon. 

248  half  dollars. 

c.  484  pounds  of  coffee  @  25  cents  per  pound. 

484  quarter  dollars. 

d.  620  bushels  of  apples  @  $1.50  per  bushel. 

e.  840  handkerchiefs  @  25  cents  each. 

f.  360  pairs  of  socks  @  25  cents  per  pair. 
g.    168  baseballs  @  50  cents  each. 

A.    440  penknives  @  $  1.50  each. 

i.     120  gallons  of  oil  @  16  cents  per  gallon. 

16  times  120. 

j.    210  pounds  of  sugar  @  6  cents  per  pound. 
k.   320  yards  of  velvet  @  $  3  per  yard. 
L    24  carpet  rugs  @  $  20  each. 
m.  180  dozen  collars  @  $  1.50  per  dozen. 
n.  44  bushels  of  wheat  @  $  1.02  per  bushel. 

44  times  $1.02. 

o.    110  barrels  of  flour  @  $  6  per  barrel. 
p.   15  horses  @  $300  each. 
q.   2  automobiles  @  $  2,400  each. 
r.    200  acres  of  land  @  $  40  per  acre. 
s.    488  pounds  of  butter  @  25  cents  per  pound. 
t.    620  geranium  plants  @  4  cents  each. 


198  SECTION  FOUR 

Cancellation 
Preparatory  Exercises 

i.  (a)  How  many  pigs  at  $  7  each  will  pay  for  27 
cows  at  $  35  each  ?  (6)  How  many  pigs  at  $  7  each 
will  pay  for  28  cows  at  $  34  each  ? 


A    LONG    METHOD 

(a)     $35 

In  (a)  the  value  of  the  cows  is  27  x  ^ ' 

times  $35,  or  $945.     The  quotient  245 

of  $945  by  $7  gives  135  as  the  70 

number  of  pigs.  $  7)1T945 

Ans.  135  (pigs) 
Find  the  answer  to  (6)  by  this  method. 


Examples  involving  only  multiplication  and  divi- 
sion can  sometimes  be  shortened  by  cancellation. 


A   SHORTER   METHOD 

In  (a)  indicate  the  product  of  35  by  27,  by    35  x  27 
placing  the  multiplication  sign  (x)  between  n 

them.     Indicate  that  this  product  is  to  be  di- 
vided by  7  by  writing  the  latter  under  a  line  drawn  below 
the  former.     Divide  35  by  7,  canceling  both,  and  writing 

the    quotient    5    above 

5 

35  X  27  *ke  f°rmer-     The  prod- 

£-= =  135  (pigs)     Ans.    uct  of  5  and  27  is  the 

number  of  pigs,  135. 
Find  the  answer  to  (6)  by  this  method. 


CANCELLATION  199 

Written  Problems 

i.    How  many  yards  at  18  cents  per  yard  will  pay 
for  21  pounds  of  butter  at  24  cents  per  pound  ? 


PROCESS 

Indicate  the  product  of  24  (/)       j         * 
by  21  and  the  quotient  of  this  re-     rf  x  fffi  _  2 
suit  by  18.     Divide  18  and  24  by         ^ 
6,  canceling  both,  and  writing  the 

respective  quotients  3  and  4.  Cancel  3  and  21,  writing 
the  quotient  7.  Write  the  product  of  4  and  7  as  the 
number  of  yards. 


2.  How  many  pounds  of  sugar  at  6  cents  a  pound 
will  pay  for  15  pounds  of  butter  at  24  cents  a  pound  ? 

3.  How  many  pounds  of  butter  at  25  cents  a  pound 
will  pay  for  75  pounds  of  sugar  at  6  cents  a  pound  ? 

4.  How  many  pounds  of  pork  at  15  cents  a  pound 
can  be  exchanged  for  27  bushels  of  potatoes  at  50 
cents  per  bushel  ? 

5.  How  many  dozen  of  eggs  at  33  cents  per  dozen 
will  pay  for  22  pounds  of  ham  at  20  cents  per  pound  ? 

6.  When  a  6-acre  field  yields  95  bushels  of  wheat, 
what  should  be  the  yield  of  an  18-acre  field  ? 

7.  When  18  acres  yield  276  bushels  of  wheat,  what 
should  be  the  yield  of  6  acres  ? 

8.  At  the  rate  of  370  miles  in  20  hours,  how  many 
miles  would  a  freight  train  go  in  15  hours  ? 


200  SECTION   FOUR 

9.    If  16  men  require  20  days  to  do  a  piece  of 
work,  how  many  days  would  it  take  15  men  to  do  it? 


PROCESS 

Indicate    the    time    re-  * 

I  n  x  s(i\ 
quired  by  1  man,  16  times  rr  __  64  _ 

20  days;  and  the  quotient         f-j> 

of  this  product  by  15  as  the 

time  needed  by  15  men.    Divide  15  and  20  by  5,  canceling 

both,  and  writing  the  respective  quotients  3  and  4.    Write 

the  product  of  16  by  4  above  a  line  and  3  underneath  it, 

making  the  improper  fraction  ^4-,  which  is  reduced  to  21^, 

the  number  of  days. 


10 ;  If  16  men  require  15  days  to  dig  a  ditch,  how 
many  days  would  it  take  12  men  to  do  it  ? 

11.  If  16  men  can  do  a  piece  of  work  in  18  days, 
how  many  men  would  be  needed  to  do  it  in  12  days? 

12.  If  13  men   require  17  days  to  do  a  piece  of 
work,  how  long  would  it  take  39  men  to  do  it  ? 

13.  If  14  men  require  19  days  to  do  a  piece  of 
work,  how  long  would  it  take  38  men  to  do  it  ? 

14.  When  135  bushels  of  corn  are  raised  on  3  acres, 
how  many  bushels  should  be  raised  on  7  acres  at  the 
same  rate  ? 

is.  At  60  pounds  to  the  bushel,  how  many  bushels 
of  clover  seed  are  there  in  7  bags  weighing  150  pounds 
each  ? 


FRACTIONS  201 

Relation  of  Numbers 
Preparatory  Exercises 

1.  Find  ^  of  each  of  the  following  numbers : 

a.  24.W    b.  48.     c.  62.     d.  86.     e.  50.     /  70. 

2.  Find  ^  of  each  of  the  following  numbers  : 

a.  24.     b.  36.     c.  48.     d.  84.     e.  64.    /.  96. 

3.  Find  ^-  of  each  of  the  following  numbers  : 

a.  18.     6.  24.     c.  36.     d.  48.     6.  69.    /  96. 

4.  Find  |-  of  each  of  the  following  numbers : 

a.  16.     1.  20.     c.  32.     d.  40.     e.  48.    /.  80. 

5.  Find  |  of  each  of  the  following  numbers  : 

a.  15.     b.  21.     c.  33.     d.  63.     e.  90.    /.  96. 

6.  What  fraction  of  60  is  each  of  the  following  : 

a.  30?  b.  20?  c.  15?  d.  12?  e.  24?  /.  40? 

7.  What  fraction  of  48  is  each  of  the  following : 

a.     8?    6.  16?    c.  24?    d.  12?    e.  36?  /.  32? 

8.  What  fraction  of  a  foot  is  each  of  the  following  : 
a.     2  in.?      b.     3  in.?       c.     4  in.?      d.     5  in.? 
e.     6  in.?      /.     7  in.?      g.     8  in.?      A.     9  in.? 
i.     1  in.?      /   12  in.?      k.  10  in.?       J.   11  in.? 

9.  What  fraction  of  a  pound  is  each  of  the  following : 
a.     1  oz.?      b.     2oz.?      c.     3  oz.?      d.     4  oz.? 
e.     5oz.?     /.     6oz.?     g.     7  oz.?      7i.     8  oz.? 
i.     9oz.?     j.  10  oz.?     &.  11  oz.?       /.  12  oz.? 

m.  13  oz.?     n.   14  oz.?     o.  15  oz.?     _p.   16  oz.? 


202  SECTION  FOUR 

10.  What  fraction  of  24  is  : 

a.      1?  6.     5?  c.     7?  d.    11? 

e.    13?  /.    17?  gr.    19?  h.   23? 

11.  What  fraction  of  24,  in  lowest  terms,  is : 

a.   20?  6.     9?  c.    15?  d.   21? 

e.    10?  /    14?  0.   22?  h.    18? 

12.  Find  the  number  whose  one-half  is : 

a.  10.       &.  15.       c.  20.       d.  25.       e.  30.      /  40. 

13.  Find  the  number  whose  one-fourth  is : 

a.  10.       6.  12.       c.  21.       d.  25.       e.  31.      /.  42. 

14.  Find  the  number  whose  one-third  is : 

a.  12.       6.  13.       c.  15.       6?.  16.       e.  21.      /.  32. 

15.  Find  2  thirds  of  a  number  when  1  third  is : 

a.  10.       6.  11.       c.  14.       d.  24.       e.  33.      /..  44. 

is.    Find  1  third  of  a  number  when  2  thirds  are : 
a.  22.       &.  30.       c.  36.       d.  44.       e.  60.      /.  80. 

17.    Find  3  thirds  of  a  number  when  2  thirds  are : 
a.  22.       6.  30.       c.  36.       d.  44.       e.  60.      /  80. 

is.    Find  4  fourths  of  a  number  when  3  fourths  are : 
a.  12.       b.  18.       c.  24.       d.  30.       e.  60.      /.  90. 

19.  Find  the  number  when  4  thirds  are : 

a.  12.       1.  16.       c.  32.       d.  40.       e.  48.      /.  84. 

20.  Find  the  number  when  4  fifths  are : 

a.  12.       6.  16.       c.  32.       d.  40.       e.  48.      /.  84. 


FRACTIONS  203 

Oral  Problems 

1.  If  \  pound  of  butter  costs  12  cents,  what  is  the 
price  of  a  quarter  of  a  pound  ? 

2.  If  one  half  of  a  pie  costs  10  cents,  what  is 
the  price  of  a  quarter  of  a  pie  ? 

3.  If  a  girl  paid  15  cents  for 
3  quarters  of  a  pie,  what  was 
the   price  of  each  quarter  ? 

4.  How   is  the  price   of  a 

quarter  of  a  yard  found  when  you  know  the  price  of 
a  half  yard  to  be  20  cents  ? 

5.  How  is  the  price  of  1  fourth  of  a  pie  found, 
when  you  know  the  price  of  3  fourths  to  be  15  cents  ? 

6.  When  2  equal  parts  of  a  number  are  60,  what 
is  each  of  the  equal  parts  ? 

7.  When  3  of  the  equal  fields  of  a  farm  contain 
60  acres,  how  many  acres  are  there  in  each  ? 

8.  If  3  fourths  of  a  number  is  12,  (a)  what  is  1 
fourth  of  the  number  ?     (6)  What  is  the  number  ? 

9.  If  2  thirds  of  a  yard  of  goods  cost  22  cents, 
what  will  3  thirds  of  a  yard  cost  ? 

10.  If  9  in.  of  wire  cost  18^,  what  will  12  in.  cost? 

11.  If  3  fourths  of  a  foot  of  wire  cost  12  cents, 
what  will  4  fourths  of  a  foot  cost  ? 

12.  Find  the  cost  of  a  gallon  of  oil  when  3  quarts 
cost  12  cents. 


204 


SECTION   FOUR 


Fractions 


A  fraction  is  one  or  more  of  -the  equal  parts  into 
which  a  thing  is  divided. 

A  fraction  consists  of  two  numbers,  called  the 
terms  of  the  fraction,  one  written  above  the  other 
with  a  line  between  them. 

When  an  apple,  a  pie,  a  number,  etc.,  is  divided  into 
two  equal  parts,  each  part  is  called  a  half;  when  it  is 
divided  into  three  equal  parts,  each  part  is  called  a 
third;  etc. 

One  half,  one  third,  one  fourth,  etc.,  are  written : 
l,  i,  1,  etc. 


If  a  pie,  for  instance,  is  divided  into  five  equal 
parts,  one  of  these  parts  is  called  one  fifth ;  a  portion 
equal  in  size  to  two  of  these  parts  is  called  two  fifths ; 
a  portion  equal  in  size  to  three  of  these  parts  is  called 
three  fifths ;  etc. 

The  number  written  below  the  line  is  called  the 
denominator  of  the  fraction  ;  it  shows  into  how  many 
parts  a  thing  is  supposed  to  be  divided.  The  number 
written  above  the  line  is  called  the  numerator;  it 
shows  the  number  of  these  parts  that  are  taken. 

A  fraction  indicates  division :  the  numerator  being 
the  dividend  and  the  denominator  the  divisor. 


FRACTIONS  205 

Proper  and  Improper  Fractions 

A.  proper  fraction  is  a  fraction  in  which  the  number 
expressing  the  numerator  is  smaller  than  the  number 
expressing  the  denominator  ;  an  improper  fraction  is 
one  in  which  the  number  expressing  the  numerator  is 
at  least  as  large  as  the  number  expressing  the  denom- 
inator. 

i>  f  •>  5~  ?  ¥?  e*c<>  are  Pr°Per  fractions. 

-|,  -|,  J^-,  J^,  etc.,  are  improper  fractions. 

A  mixed  number  is  a  whole  number  and  a  proper 
fraction  written  together. 

1J,  3f  ,  19J,  etc.,  are  mixed  numbers. 

An  improper  fraction  may  be  reduced  to  a  whole  or 
to  a  mixed  number  by  dividing  the  numerator  of  the 
fraction  by  the  denominator. 


Sight  Exercises 

1.  Change  to  whole  or  to  mixed  numbers  : 
ABODE 

«•  ¥  ¥  ¥  tt  H 

»•  ¥  V  ¥  tt  tt 

2.  Change  to  improper  fractions  : 

A  B  c  D  E 


6. 


206  SECTION  FOUR 

Lowest  Terms 

A  change  in  the  form  of  a  fraction  that  does  not 
alter  its  value  is  called  a  reduction. 

A  fraction  is  reduced  to  lowest  terms  by  dividing 
the  numerator  and  the  denominator  by  the  largest 
number  that  will  exactly  divide  both  terms. 

Sight  Exercises 
Reduce  to  lowest  terms : 

ABODE 

&•  *          *         A         A         A 

c-      9"  T6"  "2"o~  2T  TS" 

^     12.  16.  .2J)  1_8  15 

Higher  Terms 

A  fraction  is  changed  to  higher  terms  by  multiply- 
ing both  terms  by  the  same  number. 

Sight  Exercises 

1.  Change  \  to  4ths.     To  8ths.     To  24ths. 

2.  Change  \  to  6ths.     To  9ths.     To  I5ths. 

3.  Change  f  to  6ths.     To  9ths.     To  18ths. 

4.  Change  f  to  8ths.     To  16ths.     To  24ths. 

5.  Change  f  to  12ths.     To  24ths.     To  30ths. 

6.  Change  f  to  IGths.     To  24ths.     To  40ths. 

7.  Change  f  to  IGths.     To  24ths.     To  40ths. 
a.    Change  f  to  lOths.     To  20ths.     To  30ths. 


FRACTIONS  207 

Common  Denominators 

To  add  or  to  subtract  fractions,  they  must  have  the 
same  denominator.  When  two  or  more  fractions  are 
changed  to  equivalent  fractions  each  having  the  same 
denominator,  they  are  said  to  be  reduced  to  a  com- 
mon denominator. 

Sight  Exercises 

1.  Reduce  each  set  to  fractions  having  a  common 
denominator : 

A  B 

a-  i>  ib  t  i>  t>  TO- 

b-   J>  i>  J  "2?  ^'  To 

C'    i>  ¥'  F  2"'  "6"'  I'D" 

d-  \->  i>  i  §>  ^?  i 

2.  Find  sums : 

Reduce  improper  fractions  in  results  to  mixed  num- 
bers. 

ABC 

«•  i+*  i+*  *+l 

6-  t+t  i+i  t+* 

e.  i+*  i+f  i+* 

;*  *+*  *+«  t+f 

3.  Subtract: 

ABC 

«•  i-t  i-t          i-t 


208  SECTION  FOUR 

Addition  of  Fractions 
Written  Exercises 

i.  A  boy  divided  a  strip  of  copper  into  four  pieces 
measuring,  respectively,  f  ft.,  j-  ft.,  f  ft.,  and  |-  ft. 
What  was  the  length  of  the  strip  ? 


PROCESS 

Find  the  least  common  denominator  of  £  and  -J,  reject- 
ing the  other  denominators  3  and  4,  each  of  which  is  a 
factor  of  6  or  of  8.  Test  successive  multiples  of  8,  until 
one  is  found,  24,  that  is  a  multiple  of  6 ;  24  is  the  required 
common  denominator. 

Change  each  fraction  to  24 


3. 


24ths,  writing  only  the  new 
numerators  in  a  line  under 
the  common  denominator. 
Write  the  sum  of  the  nu-  If 

merators,75,  over  the  denom-  •§- 

inator,  24.      Change  -£f  to    Ans.  §3" 
,  and  then  to  3|. 


16 
18 
20 
21 

.2-5.  =  Q_3_  _ 


2.   Add  the  following  : 

ABC 

«•  Hi+i  i+S+I  *+*+* 

i+l  +  l  i  +  t+! 


i+i+i     i+f+A 

i+l+A     *+*+*• 


+*  *+l+A  i+A+i 

17-   t  +  f  +  f  *  +  *  +  *  l  +  l  +  f 

*-  i+f+f     4+f+A     f+f+A 


FRACTIONS 
Addition  of  Mixed  Numbers 


209 


i.  A  boy  divided  a  rope  into  four  pieces  measuring 
171  yd.,  8|  yd.,  f  yd.,  20f  yd.,  and  9^  yd.,  respec- 
tively. What  was  the  length  of  the  rope  ? 


PROCESS 

Reject  the  denom-                               36 

inators2,3,and4,each                   jyi       18 

of  which  is  a  factor  of                     ft  2       od. 

9  or  of  12.     Test  suc- 

cessive   multiples    of                        9"       ^" 

12,  until  one  is  found,                   20  J      27 

36,  that  is  a  multiple                     9_5_     J5 

of  9  ;  write  36  as  the     ^ng       ^Q^       jjy. 
common  denominator. 

=  2|f  =  2| 

Change  the  fractions  to  36ths,  find  their  sum 

,  and  reduce 

the  result  to  2f.     Write  f  under  the  original  fractions 

and  carry  2  to  the  ones'  column  of  the  whole 

numbers. 

2.    Add  the  following  : 

A                     B                    C                     D 

E 

a.     6£              lOf            33J              53 

17| 

20J               5f           16               20f 

12J 

15               27i             2f               7J 

13 

3A           19               !f               9A 

r                Hr3g- 

b.  24J             30J           27                 3f 

16f 

7^           36             18f             17J 

27f 

16U             7i           124             28 

8-1 

20 


7A 


210  SECTION  FOUR 

Subtraction  of  Mixed  Numbers 
Preparatory  Exercises 

1.  What  fraction  added  to  -J  gives  1  as  the  sum  ? 

2.  What  fraction  added  to  -|  gives  a  sum  ^  greater 
thanl?  i+?=lf 

3.  What  fraction  added  to  J  gives  1J-  as  the  sum  ? 


Sight  Exercises 


Subtract  : 

A 

B 

C 

D 

a. 

1 

zi 

li 

zi 

If 

zi 

b. 

1 

li 

11 

11 

zi 

zi 

zi 

_  5 

—5. 

c. 

11 

ij 

11 

If 

zi 

ri 

zi 

zi 

d. 

zi 

li 

—  .2. 

zi 

_1 

e. 

1* 

U 

li 

If 

#  F 

H  if 

zi  zi 

if  if 

zi  zi 

if  if 

zi  zi 


zi  zi 

if  *i- 

_1            -.3.              -1              -^  -5 

4^  2.  4.  2.  4.  S 

/•     2i            3i          4i           5}           6|  7J 

zi        zi      zi        zi        zi  zi 

g.    4J            5J          6J            7^           8|  9i 

-31         -41      -51        -6*       -74  -81 

,_.._-.    O  ^  ^  O  ^  B O 


SUBTRACTION  211 

Written  Exercises 

i.    From  60^-  yards  of  iron  cable  a  man  cut  32| 
yards.     How  many  yards  were  left  ? 


PROCESS 


Since  36  is  a  multiple  of  36 


-321 


17     53 
32 


21  _    7 

36  ~~  12 


9,  36  is  the  least  common 
denominator.  Write  36,  and 
underneath  it  the  numerator 
17,  and  the  new  numerator 
32.  Since  ff  is  greater  than 

^£,  increase  the  latter  by  1,  making  it  1^,  and  change  it 
to  the  improper  fraction  -||-,  writing  the  numerator  of  the 
latter  alongside  for  convenience  in  performing  the  sub- 
traction. Take  32  from  53,  writing  the  difference,  21, 
over  the  common  denominator.  Reduce  ^  to  fa.  Write 
-fa  under  the  original  fractions  and  carry  1  to  the  ones' 
figure  of  the  subtrahend.  Say  3  and  7  (writing  7)  are 
10 ;  carrying  1  to  3,  say  4  and  2  (writing  2)  are  6. 
Test  by  adding  the  remainder  and  the  subtrahend. 


2.    Subtract.     Test : 

ABC 

a.  511  -27f            48J-27f  86J-37| 

6.  80f-16|     35f-12f  63|-36f 

d.  75* -55|            67i-49fJ-  42f-36i 

O                    *x.                                   V                   JL  O  v 

e.  30^-15^         40f-14TV  50£-20f 

23T^  80J-70J 


212  SECTION  FOUR 

Sight  Problems 

1.  From  a  tub  containing  501  pounds  of  butter 
there   were   sold   20f   pounds.     How   many  pounds 
remain  ? 

2.  What  is  the  cost  of  8  yards  of  muslin  at  10  j 
cents  a  yard  ? 

3.  How  much  is  received  for  10 J  yards  of  velvet 
sold  at  $  4  per  yard  ? 

4.  A  coat  takes  3^  yards  of  cloth  and  a  vest  -|- 
yard.     How  many  yards  are  required  for  both  ? 

5.  After  walking  2J  miles,  how  far  must  a  girl 
still  walk  to  complete  41  miles  ? 

6.  If  the  distance  around  a  running  track  is  a 
quarter  of  a  mile,  how  many  times  around  it  must  a 
boy  run  to  go  1\  miles  ? 

7.  At  40J  miles  per  hour,  how  far  will  a  train  go 
in  10  hours? 

8.  If  it  requires  3  bushels  of  seed  wheat  for   2 
acres,  how  many  acres  can  be  sown  with  30  bushels  ? 

9.  (a)  At    $  ^   each,  how   many   books   can   be 
bought  for  $  8J  ?     (6)  How  many  books  at  $  f  each 
can  be  bought  for  $  8J? 

10.  At  If  bushels  to  the  acre,  how  many  bushels 
of  oats  will  be  required  to  sow  40  acres  ? 

11.  At  the  rate  of  31 J  gallons  to  a  barrel,  how  many 
gallons  are  there  in  a  hogshead  of  2  barrels  ? 

12.  Take  three  times  1    from  100. 


REVIEWS  213 

Written  Problems 

1.  From  a  tub  containing  52J-  pounds  of  butter 
27^-  pounds  have  been  sold.     How  many  pounds  are 
left? 

2.  Find  the  cost  of  8  yards  of  dress  goods  at  56|- 
cents  per  yard. 

3.  A  man  buys  23^  yards  of  velvet  at  $  3.60  per 
yard.     How  much  does  he  pay  for  it  ? 

4.  How  much  cloth  is  required  to  make  a  suit  if 
the  coat  takes  3-|-  yards,  the  vest  %  yard,  and  the 
trousers  1|-  yards  ? 

5.  After  riding  12|-  miles,  how  many  miles  remain 
of  a  journey  of  20^-  miles  ? 

6.  If  the  distance  around  a  track  is  an  eighth  of 
a  mile,  how  many  laps  must  a  bicycle  rider  make  to 
complete  13|-  miles  ? 

7.  At  37J-  miles  per  hour,  how  far  will  a  train  go 
in  10  hours? 

8.  If  it  requires  3  bushels  of  seed  wheat  to  sow  2 
acres,  how  many  acres  can  be  sown  with  72  bushels  ? 

9.  (a)  At  $  ^  each,  how  many  books  can  be  bought 
for  $1SJ?     (b)  If  the  books  are   3  quarter  dollars 
each,  how  many  can  be  bought  for  $  18|-? 

10.  At  If  bushels  to  the  acre,  how  many  bushels 
of  seed  will  be  required  for  56  acres  ? 

11.  There   are   5J   yards   in  a   rod.     How   many 
inches  are  there  in  a  rod  ? 


214  SECTION  FOUR 

Product  of  a  Mixed  Number  and  a  Whole  Number 
Preparatory  Exercises 

1.  Add  1  and  \.     Add  12J  and  12f      Multiply 
121  by  2. 

2.  How  many  quarters   are  8   times   1   quarter? 
How  many  ones  are  8  times  J?     Multiply  $1  by  8. 
Multiply  $  1J  by  4. 

3.  What  will  8  baseballs  cost  at  $  1^  each  ? 

4.  How  many  fourths  are  8  times  3  fourths  ?   How 
many  ones  are  24  fourths  ?     |-  of  8  =  ?    8  times  f  =  ? 

5.  Multiply  7f  by  12. 


PROCESS 

7fxl2  =  92  Ans. 

Think  12  times  2  thirds  are  24  thirds,  or  8.     Carry  8 
to  12  times  7  (84),  making  92.     Write  92. 
Test  by  dividing  92  by  12. 


Sight  Exercises 
Give  products : 

A  B  C  D  E  F 

x2          x4          x6          x8          x8  x4 


b.     3J  4J  5|  6£  7|  S\ 

x3          x6          x3          x9          x6          x9 


c.     9J          8f  7f  6f  51  4j 

x5          x5          x5          x5          x6          x6 


WRITTEN   EXERCISES  215 

Written  Exercises 

i.   A  barrel  of  potatoes  weighed  24  6f  Ib.     What 
would  be  the  probable  weight  of  12  barrels? 


PROCESS 

Think  12  times  f  are  -3^-,  or  9.     Carry 
9  to  12  times  6  (72),  making  81,  etc. 

Test  by  dividing  2961  by  12.                A 
^Lf 

246f  Ib. 

£.  2961  Ib. 

2.   Find  products 

A 

a.   25jx8 
&.   46|x4 
c.    75fx8 
d.    18|xl2 

B 

17Jx8 
28f  x5 
87f  x6 
26f  x  10 

c 
331x6 
66f  x9 
93|x8 
42f  x!2 

3.    Multiply  437J  by  126. 


PROCESS  4371 

Keduce  ip,  the  product  of  £  by  126,          126 


to  31  £  by  dividing  126  by  4  (without 
rewriting  these  numbers),  and  change  |       ocoo 
to  £.     Write  31f 

Multiply  437  by  6,  placing  the  right-       $74 
hand  figure  of  the  product  in  the  ones'     437 


column.    Place  the  right-hand  figure  of     55093i  A.11S. 
the  product  by  2  tens  and  by  1  hundred 
in  the  tens'  and  hundreds'  columns,  respectively.     Com- 
bine the  partial  products. 


216  SECTION  FOUR 

4.  Find  products : 

A 

a.  36^x25 

6.  42jxl8 

c.  911x19 

d.  721x23 

s.  Multiply  275£  by  16. 


B 

C 

291  x  17 

63Jxl5 

541x31 

70£x27 

83^  x  16 

65^x26 

52^1-  x  24 

441  x  22 

275| 

PBOCESS 

16 

Find  the  product  of  £  by  16  by  mul- 

6)80 

tiplying   16   by  5,  and   dividing   the 

13(£)l 

result  by  6,  reducing  the  fraction  •§•  to 
\.     Under  this  write  the  product  of  6 

1650 

times  275,  etc. 

275 

44131    Ans. 

A 

B 

c 

a. 

48| 

X 

25 

37J 

x 

17 

64f 

X 

15 

b. 

73| 

X 

16 

82|- 

X 

14 

90f 

X 

24 

c. 

56^ 

X 

13 

62* 

X 

18 

86¥ 

X 

21 

d. 

70| 

X 

19 

58| 

X 

23 

49^ 

-X 

22 

e. 

22f 

X 

16 

41| 

X 

22 

75f 

X 

31 

/ 

31| 

X 

22 

32f 

X 

31 

54f 

X 

33 

9- 

63f 

X 

31 

23f 

X 

18 

43f 

X 

21 

h. 

45f 

X 

15 

55f 

X 

17 

32| 

X 

22 

i. 

54f 

X 

20 

34| 

X 

13 

21f 

X 

14 

MULTIPLICATION 

6.   Multiply  285  by  161 


217 


PROCESS 


Find  the  product  of  285  by  %  by  divid- 
ing 285  by  6.  Find  the  other  two  partial 
products  and  combine  the  three. 


4607^  Aw. 


25x131 


a. 

6.    52x16^ 

c.    82xl9£ 


B 
37  X  141 


63  x  171 
98 

7.    Multiply  285  by  23f 


98x211 


C 

49  x  151 
74  x  181 
87  x  45TV 


285 

23J 

Find  the  product 

PROCESS 

of  285  by  £  by 

6)1425 

OQ7/3\  1 

multiplying  285  by  5 

and  dividing  the 

"    '  \F/  2" 

result  by  6,  reducing 

the  fraction. 

855 

570 

67921    Aw. 

A 

B 

c 

a.   98x23f 

98  x  24f 

78  x  25f 

.6.    67x26f 

58  x  27f 

49  x  32f 

c.    39x33^ 

27  x  34^ 

36x4l| 

d.  47x42| 

54  x  43|- 

63  x  44^ 

e.    72x51f 

66  x  62$ 

55  x  73^ 

218 


SECTION   FOUR 


Multiplication  of  Fractions 
Preliminary  Exercises 

1.  A  boy  earned  $  \.     He  gave  \  of  it  to  his  sister. 
What  part  of  a  dollar  did  he  give  her  ? 

2.  Draw  3  circles.      Divide  one  of  them  into  2 
halves,  one  into  4  fourths,  and  one  into  3   thirds. 

3.  What  is  (a)  i  of  1?     (&)  i  of  i?     (c)  1  of  1? 


4.    Draw  two  circles.     Divide  each  into  halves. 


5.   What  is  (a)  £  of  £? 


WiofJ?     (c)Jofi? 
(d)  lofl?     (e)  lofj?     (/)  Jofi? 

6.  What  is  (a)  £  of  2  thirds  ?     (6)  £  of  3  fourths  ? 
(c)  1  of  4  fifths  ?     (d)  i  of  4  fifths  ? 

7.  At  $  J  per  yard,  find  the  cost  of  (a)  4  yards ; 
(b)  3  yards ;  (c)  2  yards ;  (d)  ^  yard ;  (e)  1^  yards. 

8.  (a)  4  times  $J  =  ?   (6)3x$J  =  ?    (c)2x$J  =  ? 


MULTIPLICATION  219 

Written  Exercises 
i.    Multiply  71  by  (a)  J;    (6)  J;    (c)  Ifc    (d)  1J; 


PROCESS 

(a)  71  xl=i/x  1  =  ^  =  31 

Change  1\  to  an  improper  fraction  and  rewrite  the 
fractions.  Place  15,  the  product  of  the  numerators,  over 
4,  the  product  of  the  denominators,  making  *£-.  Reduce 
this  to  a  mixed  number. 


Cancel  3  in  a  denominator  and  15  in  a  numerator.  Place 
the  product  of  the  numerators,  as  changed,  over  that  of 
the  denominators,  etc. 


(c)  7ixli  =  -yLx-|  =  -^=lli    Ans. 
Change  both  mixed  numbers  to  improper  fractions,  etc. 

(d)  7ixl|-=^x|=10    Ans. 

Cancel  3  and  15  by  3,  2  and  4  by  2.  Omit  1,  the  prod- 
uct of  the  changed  denominators,  and  write  only  10,  the 
product  of  the  changed  numerators. 

(e)  7lx2i  =  ^xf  =  lfA=i6£     Ans. 


2.    Multiply  : 


a. 


220  SECTION  FOUR 

Division  of  Fractions 
Preliminary  Exercises 

1.  A  man  divided  $  ^  equally  between  his  2  chil- 
dren.    What  part  of  $  1  did  each  receive  ? 

2.  If  I  have  $  6,  how  many  times  can  I  spend  (a) 
$i?     (6)  $i? 

3.  If  I  have  $  6  in  quarters,  how  many  times  can 
I  spend  3  quarters  ? 

4.  To  save  $  6,  how  many  times  must  I  save  (a) 


5.  (a)  6+-!=?     (6) 

6.  Give  quotients  : 

(a)  2)12         (6)  1)12         (c)  J)12         (d)  })12 

7.  Give  dividends  : 

(a)  211_        (6)  Jll_        (c)  !)_?_        W  J)J_ 
12  12  12  12 

8.  Give  divisors  : 

(a)  ?)48          (6)  ?)18          (c)  ?)24          (d)  ?)10 
24  24  48  40 

9.  (a)  6-1  =  6  x?     (6)6-*-i=6x?     (c)  6  +  f  = 
6x?     (d)  6^-f=6x?     (e)  6-*-f  =  6x? 

10.    Give  quotients  : 

(a)  f  )12         (6)  |)12         (c)  f  )10         (d)  f)12 


DIVISION  221 

Written  Exercises 

i.    At  $  1  -J  per  yard,  how  many  yards  of  cloth  can 
.be  bought  for  $  9|  ? 


PROCESS 

The  number  of  yards  is  the  quotient  of  9f  by  1£. 
(a)  (6)  (c) 

13 

9}-*- 1*  =  ¥-5-f=^xf  =V  =  6i  (yd,) 

2 

In  (a)  indicate  the  division  of  the  mixed  numbers.  In 
(&)  rewrite  the  mixed  numbers  as  improper  fractions.  In 
(c)  indicate  the  multiplication  of  the  dividend  by  the 
divisor  inverted.  Perform  the  indicated  multiplication. 

TEST 
Multiply  the  quotient  6|-  by  the  divisor  1£. 


2.   Find  quotients : 

ABC 
a.     9J-H6J.  19fH-29j-  83J+12J 

6.   83J-J-6|  12J-H83J  71J-1Q1 

c.  71|-5-3^  10J-*-71f  87J  H- 100 

d.  87^  -6J  12J-J-87J 

e.  37^  +  3^  12^-!-33J 


222  SECTION  FOUR 

Fractional  Relations 

1.  The  operation 

a.  Of  finding  2  times  8  is  indicated  thus  :  2  x  8. 

&.  Of  finding  2J  times  8  :  2J  x  8. 

c.  Of  finding  2|  times  8  :  2f  x  8. 

d.  Of  finding  \  times  8  :  ^-  x  8. 
6.  Of  finding  j-  times  8  :  f  x  8. 
/  Of  finding  f  of  8 :  f  x  8. 

2.  Each  of  the  foregoing  is  a  multiplication  exam- 
ple, even  if  one-half  of  8  is  obtained  by  dividing  the 
latter  by  2. 

3.  The  operation  of  finding  the  number 

a.  That  produces  16  when  multiplied  by  2  is  indi- 
cated thus:  16-*- 2. 

&.  That  produces  20  when  multiplied  by  2^: 
20-21. 

c.  That    produces    22   when    multiplied   by   2f : 
22+2f. 

d.  That  produces  4  when  multiplied  by  \ :  4  -4-  J. 

e.  That  produces  6  when  multiplied  by  f :  6  •+•  f . 

4.  The  operation  of  finding  the  number 

a.    Of  which  4  is  J  is  indicated  thus :  4  -*-  J. 
&.    Of  which  6  isf :  6-*-£. 

5.  Each  of  the  foregoing  is  a  division  example,  even 
if  8-*-  \  is  obtained  by  multiplying  the  former  by  2. 


REVIEWS  223 

Oral  Problems  —  One  Operation 

State  the  operation  required  to  solve  each  of  the  following 
examples  when  the  given  numbers  are  employed. 

1.  When  dress  goods  are  48  cents  a  yard,  what  is 
the  cost  of  |-  yard  ? 

2.  When  |-  pound  of  coffee  costs  18  cents,  what  is 
the  price  of  a  pound  ? 

3.  When  tea  is  60  cents  a  pound,  how  much  can 
be  bought  for  90  cents  ? 

4.  What  part  of  a  book  of  60  pages  have  I  read 
when  I  have  completed  40  pages  ? 

s.  What  is  ^  of  84  ? 

6.  What  fraction  of  84  is  49  ? 

7.  40  is  |-  of  what  number  ? 

8.  24  is  what  fraction  of  32  ? 

9.  55  contains  15  how  many  times  and  what  frac- 
tion of  a  time  ? 

10.  10  is  what  fraction  of  15  ? 

11.  How  many  quarter  pints  of  ice  cream  are  there 
in  3  pints?     If  a  boy  eats  |-  pint,  how  many  boys 
will  eat  3  pints  ? 

12.  How  many  times  can  I  take  a  quarter  out  of  a 
box  containing  6  dollars  in  quarters?     How  many 
times  can  I  take  3  quarters  out  of  the  same  box? 
How  many  times  can  I  take  out  2  quarters  ? 


224  SECTION   FOUR 

Written  Problems 

NOTE.     First  indicate  the  solution  by  placing  the  proper 
sign  between  the  given  numbers. 

1.  When  cloth  is  96  cents  a  yard,  what  is  the  cost 
of  |-  yard  ? 

2.  When  j  pound  of  tea  costs  45  cents,  what  is 
the  price  of  a  pound  ? 

3.  When  dress  goods  are  64  cents  a  yard  how 
many  yards  can  be  bought  for  88  cents  ? 

4.  What  part  of  a  book  of  64  pages  have  I  read 
when  I  have  finished  24  pages  ? 

5.  (a)  What  is  JJ-  of  96  ?     (6)   Jfofl44? 

6.  What   fraction   of    96    is    (a)    44?      (5)    72? 
(c)   36? 

7.  72    is  (a)    if   of    what    number?     (6)  ^   Of 
what? 

8.  64  is  what  fraction  (a)  of  96  ?     (&)  Of  144  ? 

9.  How  many  times  and  what  fraction  of  a  time 
does  448  contain  160? 

10.  (a)  128  is  what  fraction  of  160?     (6)   156  is 
what  fraction  of  160  ?     (c)  20  is  what  fraction  of  64  ? 

11.  (a)  How  many  quarter  pints  are  there  in  27 
pints  of  ice  cream  ?     (&)  Among  how  many  boys  can 
27  pints  be  divided  if  each  receives  3  quarter  pints  ? 

12.  How  many  |-  inches  are  there  (a)  in  12  inches  ? 
How  many  are  there  (6)    in   18    inches?     (c)    In  1 
yard? 


DECIMALS  225 

Decimals 
Preparatory  Exercises 

1.  In  'writing  $83.17,  how  many  dollars  does  the 
8  represent  ?     The  3  ?     What  part  of  a  dollar  is  rep- 
resented by  the  1  ?     By  the  7  ? 

2.  What  part  of  a  dollar  is  17  cents  ?     How  many 
cents  are  there  in  ^j-  of  a  dollar  ? 

3.  Express  as  dollars  and  cents  : 


4.  Express  as  dimes  and  cents  : 

$0.77.         $0.49.         $0.82.         $0.03. 

5.  Express  as  tenths  of  a  dollar.      As  hundredths 
of  a  dollar  : 

$0.40.         $0.10.         $0.30.         $0.50. 

6.  What  part  of  a  dollar  is  30  cents,  70  cents,  10 
cents,  90  cents  ? 

7.  Express  as  hundredths  of  a  dollar  : 

$0.37.         $0.13.         $0.75.         $0.84. 

8.  In  the  expression  $  333.33,  how  many  dollars 
are  represented  by  the  left-hand  3  ?     By  the  next  3  ? 
By  the  next  3  ?     What  part  of  a  dollar  is  represented 
by  the  next  3  ?     By  the  right-hand  3  ? 

9.  Read  $  333.33  as  dollars  and  the  fraction  of  a 
dollar.     Read  $  33.30  as  dollars  and  the  fraction  of  a 
dollar,  expressing  the  fraction  in  lowest  terms. 


226  SECTION  FOUR 


Notation  and  Numeration 

Fractions  such  as  ^,  J,  ^,  etc.,  are  called  common 
fractions  ;  fractions  whose  denominators  are,  10,  100, 
1,000,  and  the  like,  are  sometimes  called  decimal  frac- 
tions, such  as  -ffr,  -J^L,  j^Q-,  etc. 

These  fractions  are  called  decimals  when  they  are 
written  without  denominators,  the  prefixed  decimal 
point  showing  that  they  are  fractions. 


M  H  O  Q  H  M 
111.11 


The  number  111.11  is  read  one  hundred  eleven, 
and  eleven  hundredth s,' the  word  "and"  being  used 
between  the  whole  number  and  the  decimal. 

The  number  23.4  is  read  twenty-three,  and  four 
tenths. 

The  number  256.03  is  read  two  hundred  fifty-six, 
and  three  hundredths. 

The  number  .7  is  read  seven  tenths;  the  number 
.56  is  read  fifty-six  hundredths;  the  number  .09  is 
read  nine  hundredths. 

In  the .  expression  $123.45,  how  many  times  is 
the  value  expressed  (a)  by  5  contained  in  the  value 
expressed  by  4  ?  (6)  The  value  expressed  by  4  in  that 
expressed  by  3  ? 


REDUCING  DECIMALS  227 

Reading  and  Writing  Decimals 

1.  Read  the  following : 

a.  103.27  /  983.41 

1).  .5  g.  .22 

c.  20.03  h,  6.15 

d.  .87  i.  32.08 

e.  864.09  j.  .7 

2.  Write    as   decimals   or  as  whole   numbers  and 
decimals : 

a.    One  hundred  nine,  and  nine  hundredths. 

1}.    Twenty-seven,  and  seventy-three  hundredths. 

c.  Five  tenths. 

d.  Sixteen  hundredths. 

e.  Eight  hundred  sixty-five,  and  seven  tenths. 

Reductions 
Sight  Exercises 

Express   the  following  decimals  as  common  frac- 
tions in  lowest  terms : 

A  B  c  D 

a.   .02  .25  .75  .22 

6.    .5  .4  .04  .05 

c.  .08  .84  .45  .38 

d.  .95  .8  .12  .18 

e.  .6  .85  .2  .06 


228 


SECTION   FOUR 


Written  Exercises 

Write  the  following  common  fractions  as  decimals 
A  B  c  D 

*  i  *  A  if 

^  A-  A  *  41 

*      f  ^§"  tt  TD 


i.    Give  sums : 


Sight  Exercises 


2 

+  3 

.5 
.5 

2 
+  3 

.05 
.05 

2 

+  3 

.2 

.25 

Ans. 

Omit  a  final 
decimal     cipher 
in    giving     the 
answers. 

6 

Ans. 

5 

.1  Ans. 

5 

.45 

j 
1.5 
+  1.5 

1 
+  1 

B 

.25 
.75 

c 
2.5 

+  1.25 

D 

3 

+  2 

.5 

3 
+  3 

.15 
.4 

F 

3.6 
+  3.45 

G 
2.4 

+  2.7 

2.    Give  remainders : 


5 

3.5 

4.75                Vacant  deci- 

o 

.5 

-1.5 

—  1  25            ma^  P^aces  in 

2 

.5  Ans. 

2.    An 

Q  _      .          uie  subualieiiu 
*    are  considered 

to  contain  ciphers. 

9. 

8.5 

7.35 

6.5        5.55        4.7         3. 

-4.5 

-  1.25 

-4.25 

-2.5    -3.5       -1.35    -1.8 

DIVIDING  DECIMALS  229 

Multiplying  a  Decimal  by  a  Whole  Number 
3.    Give  products: 


1.23 

2.5 

3.05 

Place  the  decimal 

x3 

x4 

x2 

point  in  the  product 

3.69 

.4ns.  10.  Ans. 

6.1  Ans. 

when  it  is  reached 
in  multiplying. 

Omit 

unnecessary  ciphers. 

2.5 

2.03        3.5 

4.05      4 

.05        4.5         .25 

x3 

x4        x2 

x5 

x  4        x  4        x  8 

Dividing  a  Decimal  by  a  Whole  Number 
4.    Give  quotients : 


4)9.  2)8.1  3). 12  5)1. 


2.25  Ans.       4.05  Ans.       .04  Ans.         .2  Ans. 

Place  the  decimal  point  in  the  quotient  when  it  is 
reached  in  dividing.  Be  careful  not  to  omit  a  necessary 
cipher  in  the  tenths'  place  of  a  quotient. 


4)8.4        4)8.2        5)9.1        6)9        2)7.1       5)6. 

Miscellaneous  Exercises 
s.    Give  answers : 

ABC 
a.   2.6  +  3.4  1.25  +  1.5  2.05  +  1.7 

6.   3.4-1.6  4.25-1.5  3.25-1.07 

c.  3.4x5  1.02x5  1.24x3 

d.  5.4-5-5  1.05-1-5  .1   -s-5 


230  SECTION   FOUR 

Written  Exercises 

Perform  operations  with  decimals  in  the  same  way 
as  operations  with  dollar^  and  cents. 

Addition  and  Subtraction  of  Decimals 


To  add  or  to  subtract  decimals,  write  the 
decimal  points  in  a  vertical  line,  and  the  decimal 
point  in  the  sum  or  the  difference  in  this  same 
line. 


In  writing  results,  reject  unnecessary  ciphers. 
Thus,  write  37  instead  of  37.00,  28.5  instead  of  28.50. 

i.    Find  sums : 

ABODE 

24.03  48.94  32.  16.66  37.7 

5.6  .67  5.85  .49  25.08 

18.  13.25  .4  .8  3.4 

2.95  1.4  27.75  58.95  11.29 


2. 

Find  remainders  : 

a. 

56.38 

72.4 

63. 

86.42 

90. 

-25.49 

-5.96 

-8.88 

-19.72 

-  25.08 

b. 

45.32 

50.2 

14.06 

21.3 

37.24 

-22.66 

-7.49 

-.99 

-1.85 

-20.06 

c. 

95. 

84.3 

73.13 

62.5 

51.25 

-5.06 

-2.42 

-8.9 

-56.03 

-6.66 

DIVIDING  DECIMALS  231 

Multiplying  a  Decimal  by  a  Whole  Number 

3.  Find  products : 

In  multiplying  or  dividing  a  decimal  by  a. 
whole  number  write  the  decimal  point  in  the  re- 
sult when  it  is  reached  in  performing  the 
operations. 

ABODE 

a.  48.05  27.2  12.5  1.15  .24 

x  4  x  5  x  6  x8  x_5 

b.  37.09  56.4          23.5          3.25  .48 

x7  x2  x4  x8  x_5 

Dividing  a  Decimal  by  a  Whole  Number 

4.  Find  quotients : 

E 


A 

a.   4)90. 

B 

6)33. 

c 
4)11. 

D 

5)23.4 

6.   25)3.        48)60.       32)88.         64)^2        64jl6. 
c.   4)4.2         6)5.7         8)10.        5)1.35         8)6. 


d.   25)1.5      36)81.      16)12.      88)4.4      48)12. 


232  SECTION   FOUR 

Miscellaneous  Written  Examples 

i.  Find  the  sum  of  thirty-five  and  four  hundredths, 
six  and  seven  tenths,  twenty-nine,  three  and  ninety- 
six  hundredths. 

'  2.  Find  the  difference  between  fifty-nine  and 
eighty-three  hundredths  and  seventeen  and  nine 
tenths. 

3.  Multiply  by  five  the  sum  of  six  and  ninety-four 
hundredths  plus  twelve  and  eighty-six  hundredths. 

4.  Divide   by   forty-four    the  difference   between 
eighty-four  and  ninety-five   hundredths  and   eighty- 
seven  and  fifteen  hundredths. 

5.  After  walking  7.2  miles  and  riding  27.3  miles, 
how  far  has  a  man  still  to  go  to  make  a  journey  of 
50  miles  ? 

6.  At  38.2  miles  per  hour,  how  far  does  a  train  go 
in  5  hours  ? 

7.  A  French  franc  is  equal  to  19.3  cents.     What 
is  the  value  in  our  money  of  a  20-franc  piece  ? 

8.  How  many  cents  are  equal  to  a  German  mark 
if  25  marks  are  worth  $  5.95  ? 

9.  If  100  pounds  sterling  are  worth  $  486.65,  what 
is  the  value  of  500  pounds  sterling  ? 

10.  A  meter   is   39.37   inches  long.     How  many 
inches  are  there  in  500  meters  ? 

11.  A  man  owns  100  acres.     How  many  acres  has 
he  after  he  buys  24.2  acres  and  sells  48.45  acres  ? 


REVIEWS  233 

Compound  Numbers 
Oral  Exercises 

1.  How  many  hours  in  .25  day  ? 

2.  How  many  minutes  in  .2  hour  ? 

3.  How  many  hours  in  .3  day  ? 

4.  How  many  hours  and  minutes  in  .3  day  ? 

5.  What  fraction  of  an  hour  is  12  minutes  ? 

6.  What  decimal  of  an  hour  is  24  minutes  ? 

7.  Add  2  Ib.  8  oz.  and  2  Ib.  8  oz. 

8.  From  3  Ib.  take  1  Ib.  8  oz. 

9.  Multiply  4  Ib.  8  oz.  by  4. 

10.  Divide  4  Ib.  8  oz.  by  4. 

11.  One  fourth  of  5  Ib.  is  how  many  pounds  and 
ounces  ? 

12.  How  many  ounces  are  there  in  4  Ib.  8  oz  ? 

is.  Change  .25  bushel  (a)  to  pecks,  (b)  To  quarts^ 
14.  What  fraction  of  a  bushel  is  (a)  1  quart  ?  (6) 
2  quarts?  (c)  3  quarts?  (d)  4  quarts?  (e)  6 
quarts?  (/)  8  quarts?  (g)  12  quarts?  (h)  16 
quarts?  (i)  18  quarts?  (/)  24  quarts?  (k)  28 
quarts  ? 

is.    Change  -|  bushel  to  quarts. 

16.  How  many  half-pint  glasses  of  lemonade  are 
there  (a)  in  a  gallon?     (6)    In  10  gallons? 

17.  How  many  inches  are  there  in  2  yards  ? 
is.    What  fraction  of  a  yard  is  27  inches  ? 


234 


SECTION  FOUR 


Avenue 
200 


§ 


100 

N 


100 


200 
Avenue 


Measurements 

1.  The  diagram  represents  a 
plot  of  ground  300  feet  long,  200 
feet  wide.     If  the  diagram  is  1 J 
inches  by  1  inch,  how  many  feet 

tj  are  represented  by  each  inch  of 
w  the  diagram  ? 

2.  (a)  How  many  square  feet 
are  there  in  the  whole  plot  ?    How 
many  square  feet  (b)  in  Ml     (c) 
InP?     (d)  In.ZV?     (e)  In  0? 

3.  (d)  M  represents  what  fraction  of  the  whole  ? 
(b)  What  fraction  does  P  represent?    (c)  Nt     (d)  0? 

4.  (a)  M  is  how  many  times  JV?     (b)  JV  is  what 
part  of  M ?     (c)  ^-  is  what  part  of  J-  ?     (d)  J  is  how 
many  times  ^  ? 

5.  (d)  Into  how  many  building  lots  25  feet  front, 
100  feet  deep,  facing  the  avenue,  can  M  be  divided  ? 
(b)  Into  how  many  can  P  be  divided  ?     (c)  Into  how 
many  lots  facing  the  street  can  jJVbe  divided  ?     (d)  0? 

6.  (d)  M  and  P  together  form  what  part  of  the 
whole  plot  ?     (b)  N  and  P  ?     (c)  JV  and  0  ? 

7.  Divide  a  rectangle  4  inches  by  2  inches  into  8 
one-inch  squares,     (a)  What  part  of   the  whole  rec- 
tangle is  each  square  ?     (6)  How  many  square  inches 
in  one   half  of   the  rectangle?    (c)  In  one   fourth? 
(d)  In  one  eighth?     (e)  How  many  times  J  is  J? 
(/)  How   many  times  |  is  J? 


CUBICAL  CONTENTS  235 

Volumes 

1.  How  many  bricks  are  there  in  a  pile  3  bricks 
long,  2  bricks  wide,  2  bricks  high  ? 

2.  How  long  is  the  pile  if  a  brick  is  8  inches  long, 
4  inches  wide,  and  2^  inches  high  ?     How  wide  is  the 
pile?     How  high?  ' 

3.  How  many  cubic  inches  in  a  pile  of  bricks  2  feet 
long,  8  inches  wide,  5  inches  high  ? 

4.  How  many  cubic  inches  hi  a  peck  if  there  are 
2150.4  cubic  inches  in  a  bushel  ?     How  many  cubic 
inches  in  a  quart  ? 

5.  How  many  cubic  inches  will  a  box  contain  if  it 
measures  on  the  inside  4.2  inches  by  4  inches  by 
4  inches  ? 

6.  Find  the  contents  of  a  box  4.48  inches  by  5 
inches  by  3  inches. 

7.  (a)  How  many  cubic  inches  are  there  in  a  block 
12  inches   long,   12   inches   wide,   12   inches   high? 
(b)  How  many  cubic  inches  are  there  in  a  cubic  foot  ? 

8.  (a)  How  many  cubic  inches  are  there  in  1J-  cu. 
ft.  ?     (b)  How  many  more  cubic  inches  are  there  in 
1 J  cu.  ft.  than  there  are  in  a  bushel  ? 

9.  A  gallon  contains  231  cubic  inches,     (a)  How 
many  cubic  inches  are  there  in  7.5  gallons  ?     (b)  How 
many  more  cubic  inches  are  there  in  *l\  gallons  than 
there  are  in  a  cubic  foot  ? 


236 


SECTION  FOUR 


Business  Forms 
Bills  for  Goods  bought  at  One  Time 

i.    Copy  the  following  bill,  inserting  the  missing 
extensions  and  the  footings : 

LOGANSPORT,  IND.,  Dec.  20,  1914 
Mrs.   Wm.  Priedigkeit 
Cypress  Hills 

Bought  of  WALLACE  GODETT 
Dealer  in  Toys 


4  Dolls                                   $1.50 
6  pr.  Dolls'  Shoes                      .15 
2  sets  Dishes                             1.05 
1  Doll  Carriage 
2  boxes  Tools                              .85 
8  strings  Beads                           .10 

6 
1 

50 

g> 
$> 

Received  payment 
Dec.  20,  1914 
Wallace  Godett 
Per  S.  M.  T. 

2.  Make  out  a  bill  for  the  following  goods.  Use 
your  own  name  as  the  buyer,  and  the  name  of  a  local 
dealer  as  the  seller.  Receipt  the  bill,  adding  the  ini- 
tials of  a  classmate  as  clerk.  Do  not  use  (3)  in  the  bill. 

31  Ib.  Nuts 

If  gal.  Ice  Cream 

4|  doz.  Lemons 

6  boxes  Strawberries 

1  Pineapple 

3  Watermelons 


BUSINESS  FORMS 


237 


Goods  bought  at  Different  Times 
3.   Copy  the  following  bill,  inserting  omitted  items : 

NEW  YOKK,  April  1,  1914 
Mrs.  L.  C.  Alphin 

181  Livingston  St. 

Bought  of  F.  LOESER  &  Co. 
Dry  Goods 

Fulton  and  Bond  Sts. 


1914 

Mch. 

2 

2pr.  Gloves                     $1.15 

2 

80 

14  1/2  yd.  Muslin                   .12 

7 

3  1/3  doz.  Buttons                  .15 

15 

4  Tablecloths                       2.75 

8  pc.  Trimming                     .37  l/% 

1  Hat 

8 

— 

27 

1/2  doz.  Handkerchiefs        2.50 

4  pr.  Stockings                      .45 

81 

By  Cash 

V 

9 
10 

Balance  Due 

The  payment  of  $10  on  Mar.  31  is  called  a  payment  on 
account.  The  bill  is  settled  by  the  payment  of  the  balance  due, 
and  is  then  receipted. 

4.    Supply  dates,  names,  etc.,  for  the  following : 
|  doz.  Collars  @  $  1 .50 

3  pr.  Cuffs  @        25 1 

1  Hat  @  $  2.75 

2  Ties  @        37J0 
2  pr.  Gloves                               @        75  t 


238 


SECTION  FOUR 


Bill  for  Labor  and  Materials 

5.    Copy  the  following  bill.     Insert  missing  exten- 
sions and  the  footing.     Receipt  it  of  the  date  Oct.  3. 

CHAMPAIGN  Co.,  ILL.,  Sept.  30,  1914 


Mr.  Daniel  Carroll 


To  FRED.  CHAMBERS,  DR. 
Steam  Threshing 


Sept. 

16 

To  800  bu.  Oats                        .02 
630  "    Wheat                     .04 
slu  ton  Coal                       6.  — 
2   Teams                          3.— 
4  Men                               1.75 

16 

$ 

The  foregoing  bill  is  rendered  by  Mr.  Chambers,  who  threshes 
Mr.  Carroll's  grain.  Besides  the  charge  for  the  threshing,  the 
bill  includes  the  cost  of  the  coal  used  in  the  engine  and  also 
the  labor  of  extra  teams  and  men  supplied  by  Mr.  Chambers. 

The  abbreviation  Dr.,  debtor,  means  that  Mr.  Carroll  is  in- 
debted to  Mr.  Chambers  for  the  items  specified. 

6.  Make  out  a  carpenter's  bill  for  making  repairs. 
Use  the  following  items:    1  man,  6  days,  at  $3.75; 

1  helper,  2  days,  at  $  2  ;  1  bunch  shingles,  at  $  1.25  ; 

2  M  boards  at  $  30. 

7.  Make  out  a  bill  for  6  rolls  of  wall  paper  at  20 
cents  per  roll ;  20  yards  of  border  at  3  cents  per  yard  ; 
hanging  the  paper  at  25  cents  per  roll  and  3  cents  per 
yard  for  the  border ;  4  gallons  of  paint,  at  $  1.80  per 
gallon ;  2  days  for  painter,  at  $  3  per  day. 


BUSINESS  FORMS  239 

Miscellaneous 

8.  Make  out  bills  for  goods  purchased  as  follows: 

Date  each  the  first  of  the  month  succeeding  the  one  in  which 
the  goods  are  bought.  Use  your  own  name  as  buyer,  and  the 
name  of  a  local  dealer  or  firm  as  seller.  Receipt  each  bill, 
adding  the  initials  of  a  classmate  as  clerk.  Make  all  exten- 
sions without  using  another  sheet.  Abbreviate  quantities,  and 
omit  such  unnecessary  words  as  "  of,"  "  at,"  etc. 

a.  Jan.  5,  1915,  bought  20  pounds  of  sugar  at  5^ 
cents  per  pound ;  3  quarts  of  milk  at  8  cents  per 
quart;  Jan.  11,  4  bars  of  soap  at  15  cents  per  bar, 
1  barrel  of  flour  for  $  5.60 ;  Jan.  18,  5  pounds  of 
butter  at  32  cents  per  pound,  6  gallons  of  oil  at  16J 
cents  per  gallon. 

1}.  Nov.  2,  1915,  bought  24  pounds  of  nails  at 
6  cents  and  1  hatchet  for  75  cents ;  Nov.  8,  3  pails  at 
75  cents  each;  Nov.  11,  9  dozen  screws  at  18  cents 
per  dozen ;  Nov.  15,  gave  4  dozen  eggs  at  45  cents  a 
dozen  in  part  payment. 

9.  Make  out  the  bill  of  the  owner  of  a  dry-goods 
store  for  six  items  bought  at  one  time.     Give  credit 
on  the  bill  for  butter  and  eggs  supplied  the  same  day 
by  the  purchaser  of  the  dry  goods.     Find  the  balance 
which  is  paid  in  cash,  and  receipt  the  bill. 

NOTE.     A  bill  showing  credits  is  somtimes  called  a  statement. 

10.  Make  out  a  farmer's  statement  of  hay  and  oats 
supplied  a  storekeeper  at  different  dates.  Credit  the 
latter  with  goods  delivered  to  the  former.  Receipt 
the  statement. 


240  SECTION  FOUR 

11.  Copy  the  following  letter  : 

MADISON,  Wis.,  Mch.  17,  1914 
Martin  Haupt  &  Sons 

138-156  La  Salle  St. 

Chicago,  111. 
Gentlemen 

Kindly  ship  me  the  following  by  fast  freight : 

3  bbl.  Portland  Cement 
10  M  Shingles,  Cedar 
14  bbl.  Wire  Nails,  10's 

Your  early  attention  to  this  order  is  respectfully  requested. 
Truly  yours 

COTTIER  JONES 

R.F.D.  No.  4 

12.  Copy  the  following  reply  : 

138-156  LA  SALLE  ST. 

CHICAGO,  ILL.,  Mch.  19,  1914 
Cottier  Jones,  Esq. 

R.F.D.  No.  4 

Madison,  Wis. 
Dear  Sir 

We  have  shipped  to-day  by  fast  freight  the  goods  ordered 
in  your  favor  of  the  17th  inst. 
Inclosed  please  find  bill. 

Yours  sincerely 

MARTIN  HAUPT  &  SONS 

is.  Draw  on  the  back  of  the  first  letter  a  rec- 
tangle 6^  inches  by  3^  inches  to  represent  an  envel- 
ope. Write  on  it  the  address  given  on  the  next 
page. 


BUSINESS  FORMS  241 


MARTIN  HAUPT  &  SONS 

138-156  LA  SALLE  ST. 
CHICAGO 

ILLINOIS 


i*.  On  the  back  of  the  second  letter  draw  an  en- 
velope and  write  the  proper  address. 

is.  Frank  O'Malley  has  money  in  the  National  City 
Bank  of  Omaha.  He  owes  Smith,  Brown,  &  Co.,  of 
St.  Louis,  $  154.36  for  goods  purchased  from  them. 
He  draws  his  check  as  follows  : 

A  Bank  Check 
No.  354-  Omaha,  Neb.,  fffiul  g,  t<?f5 

NATIONAL  CITY  BANK 

Pay  to  the  order  of.  ------- 

Dollars 


Copy  the  foregoing  check. 


242  SECTION  FOUR 

16.  If  Mr.  O'Malley  wishes  to  defer  payment  for  a 
time,  he  may  make  a  promissory  note,  as  follows  : 

A  Promissory  Note 

Omaha,  Neb.,  C&fiMjL  2,  J<?/6 
Thirty  days  after  date,  J  promise  to  pay  to  the  order  of 

tfwM,,  ftiwu,  ty  <Ho.,  (Qnz  f-funcU&cl  &i^ty-foui,  ^Dollars, 

value  received,  at 
//W-&- 

100 

On  May  2,  Smith,  Brown,  &  Co.  will  collect  $  154.36 
from  the  National  City  Bank,  which  sum  will  be  de- 
ducted from  the  money  Mr.  O'Malley  has  in  the  bank. 

Copy  the  foregoing  note. 

17.  Make  out  the  bill  of  Martin  Haupt  &  Sons  for 
the  articles  ordered  by  Cottier  Jones  (p.  240),  using 
the  prevailing  prices. 

is.  Write  Mr.  Jones's  note  for  the  amount  of  the 
bill,  promising  to  pay  the  same  in  sixty  days  after 
date,  at  a  Madison  bank. 

When  Mr.  O'Malley's  check  reaches  Smith,  Brown, 
&  Co.,  they  send  the  former  the  following 

Receipt  in  Full 

St.  Louis,  Mo.,  (&fa\Jt  £,  /<?/5 
Received  of  ________  &iawk  dtTYlallv    ________  check  far 


fine,  /-fiM^dA^d  3tyhf-$<HM,  r^r^^  j!L  Dollars 


in  full  of  account  to  date. 

lob 


BUSINESS  FORMS  243 

If  Mr.  O'Malley  should  send  a  check  for  only  $  100, 
Smith,  Brown,  &  Co.  send  him  the  following 

Receipt  on  Account 

St.  Louis,  Mo.,  ftfaM>  V-,  19?  5 
Received  of c$uw&/6  Q'TWaMeu check  for 


(Swe  /i-^vyldA&ci  f^^^^^^^^--  ^L  Dollars 

100 

on  account 

$fOO  2<L  sfmith,,  Blown,  ¥  OLo. 

100 

This  indicates  that  there  is  a  balance  still  due  the 
firm  by  Mr.  O'Malley.  . 

19.  Make  out  the  receipt  in  full  sent  by  Martin 
Haupt  &  Sons  on  the  arrival  of  Cottier  Jones's  check. 

The  following  is  a  form  of 

Rent  Receipt 

Chicago,  HI.,  Tn&ti,.  30,  /q/5 
Received  of _.  7n&\tin,  /taw/fit  ¥  t/on* 

in  full  of  rent  to  date  of  premises  138- (66  L<x,  sfaltz  ^t. 

20.  Make  out  a  mechanic's  receipt,  substituting  for 
"of  rent"  the  following,  "for  services  rendered  and 
materials  furnished." 

21.  Write  a  doctor's  receipt  "  in  full  for  professional 
services  to  date." 


244 


SECTION  FOUR 


Accounts 

The  following  is  a  form  of  account  kept  by  a  boy 
who  receives  25  cents  per  day  for  tasks  performed  be- 
fore and  after  school  hours : 


CASH  ACCOUNT 


DR. 


CR. 


Feb. 

1 

On  hand 

1 

42 

3 

Repairs  to  bicycle 

75 

5 

Bananas 

05 

7 

Wages  for  week 

1 

75 

10 

Penknife 

85 

Skates 

1 

25 

14 

Wages  for  week 

1 

75 

21 

Wages  for  week 

1 

75 

23 

Materials  for  sled 

60 

27 

Book 

25 

28 

Wages  for  week 

1 

75 

Balance 

4 

67 

8 

42 

8 

42 

Mch. 

1 

On  hand 

$4\67 

The  debit  double  column,  headed  "Dr.,"  shows  all  moneys 
received,  and  the  credit  double  column,  headed  "Cr.,"  all 
payments. 

At  the  end  of  the  month  the  word  "  Balance  "  is  written  and 
a  line  is  drawn  below  it.  The  footing  of  the  Dr.  column  is 
written,  and  the  same  amount,  $8.42,  is  written  in  the  Cr. 
column.  The  difference  between  the  sum  of  the  credits  and 
$8.42  ($4.67)  is  entered  on  the  line  with  the  word  "  Balance." 
The  account  is  correct  if  the  cash  on  hand  is  $  4.67.  A  double 
line  is  drawn  to  close  the  February  account,  and  the  account  for 
March  is  opened  with  $  4.67  in  the  debit  column. 


BUSINESS  FORMS 


245 


Personal  Accounts 

Peter  Denyse,  a  farmer,  buys  goods  of  Chambers  & 
Johnson,  giving  them  produce  in  part  payment.  The 
account  in  the  books  of  the  latter  takes  the  following 
form: 


PETER  DENYSE 


DR. 


CR. 


1915 

Oct. 

1 

Brought  forward 

12 

87 

2 

To  50  Ib.  sugar                .OG1/^ 

3 

25 

3 

By  1  ton  Hay 

U 

— 

"  20  bu.  Oats               .48 

9 

60 

7 

To  10  Ib.  Coffee                .&£*/* 

15 

"  20  yd.  Muslin              -05llk 

20 

By  40  bu.  Corn             .62 

24 

80 

27 

To  Cash 

20 

— 

SO 

"  3  bbl.  Flour               6.25 

31 

By  balance 

9 

97 

58 

.',7 

58 

37 

Nov. 

1 

Brought  forward 

$9 

97 

The  Dr.  column  shows  sums  due  Chambers  &  Johnson  for 
goods  sold  Mr.  Denyse  and  a  payment  in  cash.  The  Cr.  column 
shows  value  of  goods  received  from  the  latter.  On  Oct.  31  the 
balance  Mr.  Denyse  owes  is  entered  in  red  ink.  On  Nov.  1  this 
amount  is  entered  as  a  debit. 

22.  Copy  and  complete  the  following  account,  which 
shows  how  the  foregoing  transactions  appear  on  the 
books  of  Peter  Denyse.  Debits  in  the  foregoing  ac- 
count will  appear  as  credits  in  this  one,  and  vice  versa. 
Begin  each  credit  item  a  short  distance  to  the  right  of 
the  date  lines. 


246 


SECTION  FOUR 
CHAMBERS  &  JOHNSON         DR. 


CR. 


1915 

Oct. 

•  1 

Brought  forward 

12 

87 

2 

By  50  Ib.  sugar             .06*  /2 

8 

25 

3 

To  1  ton  Hay 

14 

— 

"  20  bu.  Oats                  .48 

9 

60 

etc. 

et 

c. 

et 

c. 

31 

To  balance 

9 

97 

.  58 

37 

58 

37 

Nov. 

1 

Brought  forward 

$9 

97 

Statements 

It  is  customary  for  the  person  to  whom  a  balance  is 
due  to  render  a  statement.  This  is  frequently  done  at 
the  close  of  a  month  in  the  following  form: 

INDIANAPOLIS,  IND.,  Nov.  1,  1915 
Mr.  Peter  Denyse 

In  account  with  CHAMBERS  &  JOHNSON 


1915 

Dr. 

Oct. 

1 

Statement  rendered 

12 

87 

To  Mdse.  (as  per  bill) 

3 

25 

2 

K       ((        (i    a      <t 

2 

45 

7 

11            (I                K       ((          (( 

1 

05 

27 

"  Cash  on  a/0 

20 

— 

SO 

"  Mdse. 

18 

75 

58 

37 

Cr. 

Oct. 

3 

By  Mdse. 

23 

60 

30 

«       « 

24 

80 

48 

40 

31 

Balance  due 

$9 

97 

UNIVERSITY  OF  CALIFORNIA  AT  LOS  ANGELES 

THE  UNIVERSITY  LIBRARY 
This  book  is  DUE  on  the  last  date  stamped  "below 


.4 

JAN  1 0  1947 


. — = — r~~ 

R.  B.  RJUJNJ.8 


103 
W16 
v.l 
c.l 


*MAL  SCUOUL 

ES> 


